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Hydrogenation of Ethylene

Metallic Catalysts

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NATIONAL BUREAU OF STANDARDS A. V. Astin, Director

Hydrogenation of Ethylene on Metallic Catalysts

Juro Horiuti* and Koshiro Miyahara*

Hokkaido University

Sapporo, Japan

*Prepared under contract at the Hokaido University

Sapporo, Japan

National Standard Reference Data SeriesNational Bureau of Standards 13

(Category 6 — Chemical Kinetics)

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Library of Congress Catalog Card Number: 67-60071
Foreword

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A. V. ASTIN, Director.

Ill
-f5

,

.
Contents

Page

1. Introduction 1 2. Reproducibility of observations 2

3. Catalytic activity of various pure metals and alloys 8

4. Reaction kinetics of catalyzed hydrogenation 13

5. Reactions associated with the catalyzed hydrogenation... 17

5.1. Experimental methods 18

5.2. Modern observations 20

6. Isotopic effect on hydrogenation rate 25

7. Supported catalysts 27

8. Carbided catalysts 30

9. Reaction mechanisms 32

9.1. Dissociative mechanism 32

9.2. Associative mechanism 32

9.3. Twigg and Rideal’s mechanism 34

9.4. Jenkins and Rideal’s mechanism 35

9.5. Redistribution mechanism 36

9.6. Adsorbed state of intermediates 36

10. Current theoretical treatments 36

10.1. Outline 36

10.2. Critical review of current treatment 38

11. Statistical mechanical formulation of rates 39

11.1. Outline 39

11.2. Function a, 40

12. Statistical mechanical formulation of the associative mechanism 41

12.1.

Formulation of k(s) 41

Page

12.2. Expressions for a E and aH 41

12.3. Practical expressions of k(s) 42

12.4. Rate equations in terms of k(s) 43

12.5. Steady state of catalyzed hydrogenation 43

12.6. Rates of reaction associated with the catalyzed

hydrogenation 46

13. Estimate of A(s)’s 48

13.1. Estimate of A(I a ) 48

13.2. Estimate of A(I b) 49

13.3. Estimates of Ar(II) and A(III) 49

13.4. Rates based on the estimated A(s)’s 50

14. Application of the theory of the associative mechanism. .

. 53

14.1. Switchover in the rate-determining step 53

14.2. Activation heat of hydrogen exchange 53

14.3. Retardation of parahydrogen conversion and ‘H2—

2 equilibration by the presence of ethylene 54

14.4. The relation between equilibrium fraction, u, and

deuterium atom fraction, xH , of hydrogen 55

14.5. Changes in VA ’s with temperature and partial pres- sures of reactants 56

14.6. “Random distribution” of deuterium in ethylene and

ethane in the deuteration of light ethylene 57

14.7. Isotopic effect on hydrogenation rate 58

15. Application of the theory of absolute rates 59

16. Concluding remark 61

17. References 61

V

Hydrogenation of Ethylene on Metallic Catalysts

Juro Horiuti and Koshiro Miyahara

Reaction rate data for the catalyzed hydrogenation of ethylene, primarily in the presence of un- supported metallic catalysts, are cirtically reviewed. Reaction mechanisms are discussed in detail, and a statistical mechanical treatment of the reaction is given, according to the generalized theory

of reaction starting from the well-known procedure of Glasstone, Laidler, and Eyring. Data for singleelement catalysts and alloys are included and interpreted, as are~~data illustrating differences due

to the physical form of the catalyst (film, foil, wire, powder, and some supported systems). Problems

are discussed concerning reproducibility of experimental results over repeated runs, and as a function

of catalyst pretreatment. The data is analyzed in 29 graphs and 29 tables, some of which are very

extensive. The bibliography includes 141 references. Key Words: Critical data, ethylene, hydrogenation, metallic catalysts, reaction mechanisms,

reaction rates. 1. Introduction

The catalyzed hydrogenation of ethylene in the

presence of metallic catalysts, especially nickel,

has been a subject of intensive investigations, as a prototype of catalyzed hydrogenations of the sort,

since its discovery by Sabatier and Senderens [l]. 1 The catalyzed hydrogenation was found to be

associated with parahydrogen conversion [2], which

turned out to be a useful profile of the reaction.

In 1932 deuterium appeared as a powerful tool for

revealing further profiles of the reaction. These

profiles were traced in the early days by following

the parahydrogen content as well as deuterium

content in hydrogen by means of the thermal conductivity method developed by Farkas, Eley, and

others [3, 4]; the deuterium content was at that

time also determined by measuring the density of

water to which the hydrogen of samples in question was converted [5]. The research work has been

substantially facilitated since 1950 when the

infrared and mass spectrometers came into daily use for investigations of adsorbed states and for

the determination of deuterium content as well

as the relative amounts of different deuterocompounds.

Notwithstanding this progress in experimental

techniques, there remained a serious, unresolved

difficulty in exploring the catalyzed hydrogenation

of ethylene. Rates of the catalyzed hydrogenation

as well as of the associated reactions decline

markedly and apparently uncontrollably on repetition of the runs over the same sample of catalyst.

Few data are thus available, as they stand, for

analysis of the catalyzed hydrogenation. It has

been found, so far, that the decline in rate is caused,

not only by impurities in the reactants, e.g., mercury

vapor, or in catalysts which have escaped their pure

preparation, but also by products of a side reaction

of ethylene, i.e., its polymerization or dehydrogenated adsorption on the catalyst.

1 Figures in brackets indicate the literature references at the end of this paper.

The character of catalyzed hydrogenation depends

further on the form and condition of the catalyst,

i.e., differs for evaporated films, powders, wires,

and plates or catalyst supported on some dispersed

medium, e.g., alumina or silica gel. For instance,

ethylene is polymerized over nickel catalyst supported on kieselguhr but not over unsupported

nickel powder. Moreover, some alloy catalysts are considerably more active than either of their

components.

Films of various metals evaporated on glass walls were introduced by Beeck [6] in 1945 for the investigation of catalyzed hydrogenation. The evaporated

film had been accepted at that time as the cleanest

possible surface, and this piece of work hence raised

lively hopes of correlating the catalytic activity and

the characteristics of catalyst metals in view of the

associated difficulty mentioned above. For this

reason, more emphasis should be laid on unsupported catalysts than on supported catalysts, which

might be associated with additional complications.

We deal in this monograph mainly with the cata- lyzed hydrogenation in the presence of unsupported

catalysts, especially of evaporated films of pure

metals, and shall refer to supported catalysts just

for reference. Experimental data on the decline of

catalytic activity are first reviewed, describing

relevant methods of the experimental investigation.

Summaries are then given of the observed kinetics

of the catalyzed hydrogenation and of the different

phases of profiles of the reaction. Attempts to for- mulate a mechanism of the phenomena in question

are next reviewed, and finally the experimental

results are accounted for systematically on the basis

of the associative mechanism [7-11],

References are often made to the optimum, i.e., the point of maximum rate of the catalyzed hydrogenation with respect to temperature at given partial

pressures of ethylene and hydrogen. For the sake

of clear and concise presentation, protium and

deuterium atoms are denoted by 'H and D when they

are discriminated. When they are not, either of

1
them or their mixture is denoted by H and called

hydrogen atom. Likewise, any of ’H2 , ’HD, and D2 or their mixture is then denoted by H2 and called

hydrogen. C2 'H4 - n Dn is called deuteroethylene

where n 0, or ethylene-dn inclusive of light ethyl- ene for which n — 0; any of them or their mixture

is denoted by C2 H4 and called ethylene, where no

discrimination is made. A similar terminology is used for ethane. The catalyzed additions of ’H2 and

D2 to ethylene are called hydrogenation with light

hydrogen and deuteration, respectively, when dis- criminated, and both of them are called hydrogenation when not discriminated.

2. Reproducibility of Observations

The catalytic activity declines, as mentioned in

the introduction, when a run of catalyzed hydrogenation of ethylene is repeated with the same

sample of metallic catalyst. This effect is especially

pronounced in case of unsupported catalysts. It is prerequisite for a reasonable study of the catalyzed

hydrogenation to elucidate the nature of this

decline. The present knowledge about it is reviewed

in the following in terms of experimental results

and comments upon or inference from them; ex- perimental results are numbered as 2.1, 2.5.1, etc.,

and comments or inferences are denoted similar!)

except that the second figure of the mark is replacec

by a Roman capital letter, e.g., as 2. A, 2.D.1, etc.

2.1. Beeck [6] used metal films evaporated on a

glass wall kept at — 183 °C and showed that, when

the films were contacted preliminarily with ethylene,

the rate of the catalyzed hydrogenation at 0 °C

decreased, on the metals indicated in parentheses,

to 10 percent (Ta), 20 percent (W), 40 percent (Ni), or 95 percent (Pt, Rh) of the rates without the preliminary contact in the respective cases.

2.2. The rate of the catalyzed hydrogenation depends

on the sequence in which reactant gases are introduced over the catalyst. Toyama [12] observed

the rates of three consecutive runs conducted over

a sample of nickel powder reduced from its oxide

(termed reduced nickel in what follows), introducing

in the first run hydrogen and ethylene simultaneously, in the second hydrogen in advance and in

the third ethylene in advance; each run was con- ducted after evacuating the product of foregoing

run. In the second and third runs, the catalyst was

left overnight at room temperature in contact with

the reactant gas introduced in advance before the

other was admitted. The second run gave a rate higher than the first, while the third run gave a rate lower than both the first and second.

2. A. The third run of 2.2 confirms 2.1 in the case of

nickel, whereas the second run of 2.2 indicates a regeneration of catalytic activity by the hydrogen

treatment. The features of the decline may be

gathered from the results described next.

2.3.1. The following qualitatively coincident results were obtained when admitting repeatedly small

doses of ethylene over films of Ni [6, 13, 14], Pd [15],

W [16], or Ir [17] evaporated on a glass wall of a vessel kept at room temperature [18]. No gas what- ever was detected inside the vessel until the total

sum, Q, of the number of molecules of ethylene admitted exceeded a certain value A , when ethane

alone began to appear with further increase of Q.

When Q exceeded a certain other value B (> A),

ethylene began to appear in the gas phase. Now,

both the number of ethane molecules and the number, Q' , of adsorbed ethylene molecules ( Q minus

the total number of ethylene and ethane molecules

in the gas) increased until Q exceeded a certain

third value, C (> B), beyond which both Q' and the

number of ethane molecules remained, respectively,

constant.

Number A corresponded to 30 percent coverage

of the surfaces at room temperature provided that

the number of hydrogen atoms adsorbed at — 183 °C

[13] equaled the number of their adsorption sites

and each ethylene molecule occupied two such

sites. The number of ethane molecules formed at Q = B approximately equaled Q' at that point.

The above results are shown in figure 1 [18], where

the respective values, of Q, A, B, and C, are indicated with vertical broken lines.

MOLECULES OF C

2H

4 ADMITTED ( x 10“ l6

) per mg EVAPORATED FILM

FIGURE 1 . Behavior of ethylene on evaporated nickel films [ 78 ]. C2H4 adsorbed: C2 H, admitted minus C2 H4 + C2H6 in gas.

2.3.2.

Mckee [19] found by the use of reduced

nickel of 1.41 m2 BET area that the number A in 2.3.1 increased with fall of temperature from

2
2 X 10' 7 C2 H4 molecules at —22 °C to 13X10 17 C2 H4 molecules at —78 °C, which corresponded to the increase of coverage from ca. 3 to 20 percent of

the surface. 2.4. Ethylene in contact with a metal him left on

it compounds of a composition which varied with

the temperature during contact, the extent of evacuation after contact and the sort of metal. The composition of the compounds was C2 H0 .8 at 25 °C [14]

and C at 170 °C [13] on nickel him and C2 H3 . 6 ~ 3.9 at 100 °C on Ir [17]. This process is called dehydrogenated adsorption and the compound termed

adsorbed complex in what follows.

TABLE 1. Rates of removal of adsorbed complex from evaporated

metal films by treatment with hydrogen [ 7 8 J

Metal Temp. °C Reaction time,

min

% Removed Authors

Rh 23 i 60 Beeek [14] Rh 23 long 100 Beeek [14] Pd 0 5 50 ~ 60 Stephens [15]

Ni 20 60 20 Beeek [14] Jenkins and

Rideal [13]

The product of the treatment in case of Rh was almost ex- clusively ethane, while in case of Ni 90 percent of the product were saturated hydrocarbons of carbon number 4 to 8.

2.5. 1 he adsorbed complex can be removed from

the surfaces by hydrogen treatment around room

temperature as shown in table 1 . The adsorbed

complex is not so readily removed from nickel as

it is from iridium. The removal from nickel is, on

the other hand, appreciably slower than the cata- lyzed hydrogenation on the same metal, by a factor

of several hundreds [13]. This aspect contrasts

with that of preadsorbed acetylene which cannot

by hydrogenated off nickel at 23 °C, whereas 40

percent of it can be hydrogenated off rhodium at the same temperature in 1 hr [14].

2 . 6. Thomson and Wishlade [ 20] saturated an evaporated nickel film with radioactive 14 C2 H4 at 20 °C, evacuated it subsequently a little while and

followed its removal by different treatments with

radioactivity measurements. 2 percent of the radioactivity were thus lost by contacting the saturated

film with nonradioactive ethylene, another 10 percent were lost by allowing this film to catalyze the

hydrogenation of 10 cm Hg nonradioactive ethylene

with equimolar hydrogen, and the radioactivity still remaining was further diminished by 30 percent

by a hydrogen treatment. The 58 percent radioactivity thus left could not be reduced further when

allowing the film once again to catalyze the hydrogenation of nonradioactive ethylene of partial

pressure around 9 cm Hg with equimolar hydrogen.

These results contrast with those obtained by

Cormack, Thomson, and Webb [ 21 ] for aluminasupported catalysts of Ni, Rh, Pd, Ir, and Pt

saturated with 14 C 2 H4 which lost, respectively, 36.5

percent (Pd), 76 percent (Ni), 77.5 percent (Rh),

84 percent (Ir), and 93.5 percent (Pt) of the radioactivity as they catalyzed the hydrogenation of

nonradioactive ethylene.

2 .B. Results 2 . 1 , 2 . 2 , and 2.3.1 are accounted for by

assuming that adsorbed complex poisons the catalyst, and hydrogen atoms formed by the dehydrogenated adsorption of ethylene are combined with

ethylene from ethane. The number of ethane molecules at Q — B would then approximately equal Q' as

in 2.3.1, if the adsorbed complex is of composition

C2 H2 , i.e., an acetylenic complex [6], in other

words ethylene subjected to dehydrogenated adsorption gives off equimolar hydrogen which is combined with another ethylene molecule to form

ethane.

Result 2.3.2 indicates that at lower temperatures

the quantity of adsorbed ethylene has to be en- hanced in order to provoke the dehydrogenated

adsorption coupled with the hydrogenation.

Result 2.4 shows that ethylene is stripped of its hydrogen to a far greater extent over nickel than it is over iridium, while 2.5 and 2.6 show that the

adsorbed complex is less readily removed with

hydrogen treatment from nickel than from iridium.

This great difference in ease of removal is compared

with the contrasts in results 2 . 1 , viz., that the

adsorbed complex is more inhibitive of the cata- lyzed hydrogenation on nickel than on platinum

metals.

2 .C. Ethylene molecules may exchange their hydrogen atoms by way of the hydrogen atoms given

off by dehydrogenated adsorption according to the

associative mechanism [7-11] (cf. sec. 9.2) through

the half-hydrogenated state C2 H5 (a) attained by

the step

C2 H4 (a) + H(a)^ C2 H5 (a),

where (a) signifies an adsorbed state. The hydrogen

atom which has combined with C2 H4 (a) to form

C2 H5 (a) shares, according to the associative mechanism, chemically equivalent positions with two

hydrogen atoms from a methylene group of C2 H4 (a), and each of the latter two gains, therefore, the

probability 1/3 to become H(a) in the reverse of the

above step, and hence to find its way into another

ethylene molecule, as evidenced by the following

result.

2.7. A rapid exchange between ethylene-r/4 and

light ethylene was observed by Miyahara [ 22] on a freshly evaporated nickel film even at —23 °C, contrary to a negative result reported by Conn and

Twigg [23]. Flanagan and Rabinovitch [24], tracing

the experiment of Conn and Twigg [23], were able

to observe an exchange reaction at 60 °C by using

much more nickel wire than Conn and Twigg.

2 . 8. Results given next show that the dehydrogenated adsorption of ethylene occurs even in the pres273-052 O - 68 -2 3
ence of hydrogen, i.e., under the normal condition

of the catalyzed hydrogenation.

2.8.1. Jenkins and Rideal [13] observed the cata- lyzed hydrogenation of 20 mm Hg ethylene with

equimolar hydrogen at 20 °C over evaporated nickel

film for 10 min, evacuated the product and repeated

the experiment consecutively. The rates of total

pressure decrease found were 3.50 mm Hg/min in

the first run, 1.90 mm Hg/min in the second run and 1.30 mm Hg/min steadily in the third and several subsequent runs. When they contacted the

evaporated film preliminarily with ethylene, the

steady value (1.30 ~ 1.60 mm Hg/min) was obtained

throughout from the first run on.

2.8.2. The catalytic activity of metal films is appreciably reduced by impurities, especially mercury

[25] and oxygen [22, 27]; the former also diminishes

the adsorption of hydrogen on metal films. Mercury

is liable to' be introduced into a reaction vessel

along with reactant gases [26] and in consequence

accumulates on the metal film. A trace of oxygen

amplifies the decline of catalytic activity when the run of catalyzed hydrogenation is repeated [22],

creating, besides, an induction period as seen in

figure 2(a) [22]. Figure 2(b) [22] shows that a nearly

reproducible rate of hydrogenation is secured by

removing the impurities.

Figure 2(a). The courses of repeated hydrogenations of ethylene

with ca. equimolar hydrogen contaminated with oxygen at 50 °C over evaporated nickel film [22]; mercury excluded.

2.8.3.

Miyahara [26] determined, under the pure

conditions attained in 2.8.2, the quantities, QE and

(/H , of ethylene and hydrogen adsorbed, respecFlGURE 2(b). The. courses of repeated hydrogenations of ethylene

with ca. equimolar pure hydrogen at 50 °C over evaporated

nickel film [22]; mercury excluded. Table 2. Number of moles of ethylene (QE) and hydrogen (QH) adsorbed on evaporated nickel films in course of hydrogenation

of ethylene by equimolar hydrogen [26].

Initial total pressure: ca. 0.1 mm Hg

Temp. °C Surface of evaporated

Ni film Qe X 108 £>h x 108

0 F 17.1 5.5 F 16.8 4.5 S 15.4 6.5 S 17.6 3.3 c 13.1 1.7

101 F 15.6 1.3 F 10.0 2.7 s* 9.8 - 8.8 s 11.6 2.2 c 9.5 0.5

145 F 9.6 -9.6

s 11.4 0.8 c 10.0 0.0

A given run of catalyzed hydrogenation were conducted over

nickel films evaporated on the wall, kept at 200 °C, of a reaction vessel of 120 cm3 capacity, by admitting the reactant gas mixture

into the reaction vessel. Such a run was followed in some cases by another on evacuation of the product of the foregoing run. The films thus used were kept at 500 °C in H2 of few mm Hg for an hour, evacuated at the same temperature to 10“ 7 mm Hg and

then coated with new evaporation of nickel, and one or two runs were similarly conducted over the newly coated films. The sur4
face of a film either freshly evaporated or freshly coated is signi- fied by F, and that used once as above by S; C refers to a surface used several times consecutively at 200 °C, each such run was

preceded by an evacuation at the same temperature, until the

rate decreased from that over F by a factor of several tens. Qe and QH were determined, as the excess of the number of moles of ethylene and hydrogen initially introduced into the reaction vessel over that of ethylene and hydrogen remaining in gas plus that combined in ethane, on the basis of the experimental

result [61] that the adsorption of ethane is inhibited by ethylene.

Gas mixtures were sampled for QE

- and (^-determinations

immediately after the measurement of the initial rate of total pressure decrease, which lasted a few seconds just after the

introduction of the reactant gas mixture, except in a run marked

with asterisk; gas mixture was sampled in the latter case toward

the end of the run, when the total pressure decreased no longer

perceptibly.

tively, in course of the progress of catalyzed hydrogenation, as shown in table 2. F and S in the table

refer to the surfaces of freshly evaporated films or those once used for a run of hydrogenation, and C

refers to surfaces used several times consecutively

at 200 °C until the rate of hydrogenation over them

decreased from that over F by a factor of several

tens. C exhibited every characteristic of the “carbided surface” [13] which was obtained by exposing

a freshly evaporated film to ethylene at 200 °C for

10 min.

2.D. The dehydrogenated adsorption of ethylene in

the presence of hydrogen is evidenced by the negative value of (2h i n table 2, which indicates a net

evolution of hydrogen, its absolute value being a

lower limit to the amount of hydrogen evolved by

dehydrogenated adsorption. A negative QH was

observed over F as well as over S surfaces at temperatures above the optimum temperature, 30 °C, as seen in the table [26J. It follows that dehydrogenated

adsorption occurs side by side with the catalyzed

hydrogenation above the optimum both over F and

S surfaces.

2.9. The following further data on the dehydrogenated adsorption of ethylene are available.

2.9.1. Miyahara [26] observed the distribution of

deuterium in ethylene and hydrogen in the initial stage of catalyzed deuteration of fight ethylene as shown in table 3 under the pure conditions established in 2.8.2. The optimum temperature for an

equimolar mixture of ethylene and deuterium of

0.1 mm Hg initial total pressure was found 50 °C in

this case. 'FE was evolved in case of F but not ol S

at temperatures below the optimum (—45 and — 23 °C), whereas ^2 was evolved above the optimum in both the cases.

2.9.2. Formation of ethane from ethylene caused

by its dehydrogenated adsorption on reduced

nickel was almost suppressed, according to Hirota

and Teratani [28], by a preliminary adsorption of

CO2 , which covered 30 percent of the BET area

of the reduced nickel, whereas the same preliminary

adsorption on the same catalyst was almost ineffective with respect to catalyzed hydrogenation.

Table 3. Relative amounts of ethylenes-dn = En and hydrogens-dn = Hn in the product of deuteration of light ethylene over evaporated

nickel films [26]

React,

temp. °C

State of

film surface

Deuterated

% C2 H4 Deuterated

% C2 H4 min -

1

Relative amounts

Deuterium atom

fraction in En in C2 H4 , % Hn in H2 , %

E0 Ei e2 e3 e4 •h2 •HD d2 c2 h4 h2

— 45 F 4 9.7 63 31 7 0 0 8.5 22.5 69 0.112 0.803 S 2 3.5 93 7 0 0 0 0 1.6 98.4 0.017 0.992 -23 F 15 31.8 57 34 9 0 0 10 25 65 0.130 0.775 S 10 18.2 90 10 0 0 0 0 1.6 98.4 0.025 0.992

0 F 35 74.3 44 36 18 2 0 11 26 63 0.195 0.760 S 20 56.9 64 30 6 0 0 0 6 94 0.105 0.970

28 F 40 110.3 45 38 14 2 0 11 30 59 0.180 0.740 S 43 98.0 66 28 5 1 0 2 10 88 0.103 0.930

32 F 45 129.7 49 34 11 7 0 11 22 67 0.165 0.780 S 41 107.1 40 36 20 4 0 10 19 71 0.220 0.805

75 F 40 102.1 21 35 28 13 3 30 42 28 0.355 0.440 S 38 97.0 29 38 24 7 2 30 29 41 0.263 0.695 no F 18 54.0 16 32 32 16 4 11 39 50 0.400 0.695 S 21 50.2 21 29 37 10 2 14 39 47 0.340 0.665

“Deuterated percent C2 H4 ” in the third column represents the percentage decrease of the sum of the numbers of moles of

4 C2 H4 = ^ E„ from the sum at the beginning of the catalyzed hydrogenation, when C 2 H4 is practically exclusively CVH4 . F denotes

n = 0 the surface of freshly evaporated film and S that used once for a run; cf. legend of table 2.

5
2.E.I. The dehydrogenated adsorption will lead to an evolution of 'H2 as in 2.9.1, if it consists simply

of a release of hydrogen molecules into the gas. If

it supplies, on the other hand, hydrogen in an

intermediate state of the catalyzed hydrogenation,

e.g., H(a) directly, then 'H2 will also appear in the

gas as a product of conversion of this intermediate,

unless steps consuming it are rapid enough to suppress the conversion, e.g., to inhibit the recombination of the H(a)’s by lowering their activity.

It follows now from the observed absence of J H2 evolution over S surfaces below the optimum that

dehydrogenated adsorption occurs neither under

immediate release of hydrogen molecules nor to evolve them through the intermediate state. Under

the latter conditions the dehydrogenated adsorption,

if any, may be traced by a deviation from the

stoichiometry of normal hydrogenation; the total

pressure would not then decrease, in case of cata- lyzed hydrogenation of ethylene with excess hydrogen in a constant volume, as far as corresponding

stoichiometrically to the exhaustion of the ethylene.

On account of absence of such a deviation (cf. 4.1),

the dehydrogenated adsorption is concluded to be

practically suppressed on S surface.

The validity of the above arguments rests upon

the postulate that the hydrogenation and the dehydrogenation of ethylene are exclusively reactions

occurring on metallic catalysts. This is assumed

throughout in what follows.

2.E.2. It follows from the preferential inhibition of

dehydrogenated adsorption observed in 2.9.1 that

the two reactions do not occur on the same site,

insofar as both reactions on their respective sites are admitted to be blocked solely by the product,

adsorbed complex, of dehydrogenated adsorption.

It is induced from this conclusion and 2.9.2 that the

nickel catalyst’s surface consists of two parts, (d)

and (h), which catalyze the dehydrogenated adsorption and hydrogenation, respectively; 2 the former

remains poisoned by adsorbed complex if it is on an S surface below the optimum (2.9.1) and also by

C02 (2.9.2) [28],

2.10. Experimental results are reviewed next from

which diverse theories are derived on the state of

catalyst’s surface.

2.10.1.

Crawford, Roberts, and Kemball [29] an- nealed nickel films, evaporated on glass walls kept

at —195 °C, at different temperatures from 0 to 400 °C and observed their activity in catalyzing

both the hydrogenation with ’H2 and the deuteration

of light ethylene. The rate of hydrogenation with

1 H2 decreased when the runs were repeated on the

same surface but their rates per unit BET area remained constant for a definite annealing temperature and decreased only with rise of the annealing

temperature. Both the activation heat of hydrogenation with *H 2 and the deuterium distribution

2 The two parts may be attributed to different lattice planes exposed on the catalyst surface; cf. 2.11.1.

in the ethane formed by the deuteration remained

unchanged throughout [29].

2.10.2.

The BET area referred to in 2.10.1 decreased

by a little over 40 percent when contacting the film

with ethylene as shown in table 4, irrespective of

the annealing temperature.

Table 4. Change of BET area of evaporated nickel film by

adsorption of C2 H4 at —80 °C [29]

Annealing

temp. °C

Volume of C 2 H4 adsorbed cm3 (S.T.P.) x 103

BET area cm2 X 10 -2

Before adsn.,

i

After adsn.,

2

0 20 23.2 12.8 25 12 19.6 11.0 too 8 13.4 7.8

2.10.3. Campbell and Duthie [30] found that the

BET area of nickel film decreased to the same

extent when allowing the film preliminarily to adsorb

N2 0, 02 , or Hg.

2.10.4. Jenkins and Rideal [13] found that nickel

surface covered by acetylenic complex and preliminarily evacuated, evolved hydrogen, amounting

to be equimolar with the acetylenic complex,

as temperature was raised gradually from 20 °C

up to 170 °C in a closed space. On cooling it down

to room temperature the evolved hydrogen was

absorbed, but not completely.

2.10.5. Foss and Eyring [27] found the rates of

consecutive runs of hydrogenation to be reproducible on a carbided nickel surface 3 when this was

treated with 5 cm Hg hydrogen at 250 °C for 30 min

before every run. The reproducible rate thus established was about one half that on a freshly evaporated film but was several tens of times larger

than that on a carbided surface (see footnote 3)

not treated with hydrogen.

2.10.6. A preliminary contact of the catalyst in 2.10.5 with ethylene retarded the hydrogenation

in the beginning of its course, but did no longer

so several minutes later [27].

2.F. Kemball et al. [29]. attributed the decrease of

BET area in 2.10.1 and 2.10.2 to a sintering of the

catalyst’s surface caused by the heat of hydrogenation or adsorption but did not take into account the

effect of adsorbed complex. Campbell and Duthie

[30] referred the effect, on the basis of 2.10.3, to the adsorbed complex, which was suggested to decrease the quantity of krypton adsorbed in BET

measurements, thus simulating a reduction in BET

area, although their reason why it should decrease

the adsorption of krypton does not appear clear.

Result 2.9.1 speaks definitely against sintering as responsible for the rate decrease. The decrement

3 Cf. 2.8.3.

6
of the rate between F and S in 2.9.1 becomes

monotonously smaller with rise in temperature; it falls from 64 percent at —45 °C to 8 percent at 110 °C, as seen in table 3. If sintering was responsible for the decline in rate, its extent and in

consequence the rate decrement ought to be the

greater, the higher the reaction temperature and

the greater the rate of heat evolution, i.e., the

reaction rate times reaction heat per mole. The

reaction rate increases from —45 to 32 °C monotonously by a factor of more than ten, as seen in the

same table, and the reaction heat per mole, though

slight, increases as well. The decrement of rate should hence increase monotonously with rise of

temperature. This is quite contrary to the experimental result, and the sintering can, therefore, not

be responsible for the decrease in rate.

It appears, however, necessary to regard 2.10.1,

2.10.2, and 2.10.3 with caution, in view of 2.8.2,

because of a possible intrusion of mercury, which

has been positively evidenced under similar experimental conditions [311.

Jenkins and Rideal [13] attributed the result of

2.10.4 to the migration of carbon atoms from the

surface into the bulk of metal so that a clean metallic

surface, available for adsorption of hydrogen,

was regained. However, results 2.10.5 and 2.10.6,

backed by 2.5 and 2.6, indicate the substantial

effect of hydrogen in recovering a catalytically

active metallic surface from the carbided surface.

These results lead to the view, amplifying upon

2.E.2, that the treatment before every run in 2«10.5

released part (h) from the poisoning due to the foregoing run, leaving part (d) steadily poisoned so as to secure the reproducibility of the results.

2.11. The following results might provide further

informations relative to the dual catalyst surface

advanced.

2.11.1. Cunningham and Gwathmey [32] observed

the activity of individual lattice planes of nickel

single crystal in catalyzing the hydrogenation of

ethylene from 50 to 200 °C, preliminarily treating

the lattice planes with hydrogen at 500 °C. They

found that (321) > (111) and (110) > (100) as shown

in figure 3, where the Miller indices represent the

relevant activities. They also observed that lattice

planes other than (111) and (100) lost their metallic

luster by contact with ethylene at 450 °C, which

they termed carbon deposition.

2.11.2. Farnsworth and Woodcock [33] observed

effects of heating in high vacuum, bombardment

with Ar+ ions etc., on the activity of nickel and

platinum plates in catalyzing the hydrogenation of

ethylene with equimolar hydrogen at 0.1 to 1.0 mm

Hg total pressure. The results are shown in table 5,

where the catalytic activity is given in terms of the

first order rate with respect to hydrogen partial

pressure. The table shows the enhanced activity

due to heating in high vacuum and bombardment

in treatments (1) and (3), which is all but lost again

by annealing at 550 °C as seen in treatments (2),

(4), and (5).

TABLE 5. Rates of hydrogenation of ethylene over catalysts of

diverse pretreatments [33].

Pretreatments

Activity (arbitrary units)

Ni catalyst Pt catalyst

(1) Heat-treated and quenched 45 ±5 2400 ± 200

(2) Heat-treated, quenched, and 17 ± 2 750 ±30

annealed.

(3) Bombarded with positive argon 700 ±100 2200 ±200

ions.

(4) Bombarded and annealed 8±2 200 ±30

(5) Bombarded, heat-treated,

quenched, and annealed. 7±2 225 ±30

Approximate temperature of: heat-treatment of nickel, 850°; annealing nickel, 500 to 550 °C; heat-treatment of platinum, 1050

to 1350°; annealing platinum, 700°. Quenching was always pre- ceded by an induction heat-treatment of at least one-half hour to insure uniformity in surface structure of the catalyst preceding

the quenching. The quenching was accomplished by suddenly

stopping the induction heating current and allowing the catalyst

to cool in vacuum to room temperature.

Farnsworth and Woodcock attributed the en- hanced activity to lattice defects created by the

treatments (1) and (3) in table 5 [33].

2.G. The following are general conclusions regarding the reproducibility of observations on the

catalyzed hydrogenation.

The decline of catalytic activity, though considerably reduced by purification of reactants, persists, even in the case where purest reactants are used,

which is attributed to a poison produced by dehydrogenated adsorption of ethylene, i.e., adsorbed

complex, termed acetylenic complex [6], carbide

[13], coke [34], or polymer [34]. It is induced from

experimental results that the catalyst surface

consists of two parts: one part (d) causes the dehydrogenated adsorption of ethylene, is readily

poisoned by adsorbed complex and is not readily

recoverable; the other part (h) catalyzes the hydrogenation, is but slowly poisoned and readily

recoverable.

The carbided surface [13] shows no decline of

catalytic activity at all, which might hence appear

pertinent to the investigation of the catalyzed

hydrogenation. The carbided surface might, however, be substantially degenerated from the genuine

metallic surface, on account of the considerable

differences in their properties as discussed in section 8. To the best of our present knowledge it appears that catalyzed hydrogenation on a genuine

metallic surface is observed with an S surface below

the optimum, provided that the reactant gases are

rigorously freed from impurities, especially mercury

and oxygen. Above the optimum, where hydrogenation and dehydrogenated adsorption are simultaneously going on, it would be necessary for the

elucidation of the catalyzed hydrogenation to find a reasonable way to analyze the observed overall

reaction with respect to the two individual reactions.

7
TIME , min.

FIGURE 3. Activities of crystal planes of Ni in catalyzing the hydrogenation of ethylene [32].

Much more work will be necessary before hydrogenation which is associated with dehydrogenatedadsorption can be reasonably discussed on the level

of lattice planes and lattice defects of catalysts.

3. Catalytic Activity of Various Pure Metals and Alloys

The rate of catalyzed hydrogenation of ethylene

is very sensitive to the preliminary treatment of

the catalyst metal, apart from the working conditions as reviewed in 2, and this treatment must be

precisely specified, should the informations gained

be of any significance. Informations on catalytic

activities which are more or less significant in this sense are reviewed next, if not immediately assignable to intrinsic properties of the catalyst material.

3.1. Beeck observed the activity of evaporated films

of various metals in catalyzing the hydrogenation

of ethylene comparatively at 0 °C [6, 14]. The rates

8
were strictly proportional to hydrogen pressure

and independent of ethylene pressure, according

to Beeck, although no data are given [6, 14] of their

absolute magnitude. The results are shown in figure

4 and table 6 in terms of activity k, percent dcharacter of metallic bonds and adsorption heat of

reactants on the metals. The quantity k is the ratio

between the first order rate with respect to hydrogen per unit BET area on a given metal and that on

rhodium. Figure 4(a) shows that the activity in- creases generally with the percent d-character of

metals and that the activity of a Ni film with the

preferred orientation of the (110) lattice plane

parallel to the glass base, marked with (110), is ca. four times as large as that of a Ni film with random

orientation of crystallites. Figure 4(b) shows that

Rh is the metal at the maxima of both the activity

and percent d-character and at the minima of the

adsorption heats of both ethylene and hydrogen.

The results obtained by Beeck [6, 14] have been

commented upon from a variety of aspects as below.

3.1.1. Phenomenologically, a linear relation was

advanced by Schuit [35] between logio k observed

by Beeck [6, 14] and the product of percent d-character and the valency of metals according to Pauling

[36], as shown in figure 5. 3.1.2. The closest distance between two Rh atoms

is 2.69 A in its fic.c. crystal of lattice constant 3.80 A

indicated in figure 4(b). This closest distance is nearly coincident with the ideal metal-metal distance, 2.73 A, for the associative adsorption 4 of

ethylene without strain as calculated by Twigg and

Rideal [37] assuming the carbon-metal distance to be that in nickel carbonyl, 1.82 A. Notwithstanding

this nice agreement, our present theoretical equipment appears not replete enough to afford a consist- ent explanation of the maximum activity at rhodium

in this way.

3.1.3. Beeck [14] suggested that the rate of catalyzed

hydrogenation was controlled by the process of

hydrogenated desorption, e.g., the reversal of dehydrogenated adsorption, of the adsorbed complex

which makes room for adsorption of hydrogen. This can hardly be the case, however, since the catalyzed

hydrogenation is progressively poisoned by adsorbed

4 Ethylene is assumed [37] to be held by two adjacent metal atoms breaking its w-bond

and forming two carbon-metal bonds, and all bonds of the carbon atoms are tetra- hedrally disposed like those of ethane.

complex in its course as elucidated in section 2.,

and moreover, the hydrogenated desorption is far

slower than the catalyzed hydrogenation [13] as mentioned in 2.5. 3.1.4. Ethylene is subject to the dehydrogenated

adsorption as concluded in 2.4 and 2.B and, as seen from tables 1 and 6, the less active catalyst is that

which is not easily rid by hydrogenated desorption

of the adsorbed complex thus formed and associated

with a high initial heat of adsorption [14]. 3.1.5. The activation heat of the catalyzed hydrogenation over different metals amounts uniformly

to 10.7 kcal, except in the case of tungsten where

it is 2.4 kcal/mole [6]. It follows that the catalytic

activity is proportional to the preexponential factor

for all these metals except tungsten [6, 14]. 3.1.6. An exception similar to that in 3.1.5 is found

in case of tungsten by a statistical-mechanical

analysis of kinetic data [38]. We obtain 1015 cm-2 as an order of magnitude for the number of sites of

the critical complex 5 per unit area of the catalyst’s

surface from an analysis of kinetic data of the reaction involving no hydrocarbon over tungsten, which

is in the line with the number derived from almost

all available date of more than 60 cases of reactions over other metallic catalysts; but the number was

found exceptionally low, around 106 cm-2

, in case

of the exchange reaction between methane and

deuterium over tungsten.

3.1.7. The above results, 3.1.4, 3.1.5, and 3.1.6, are accounted for on the basis of the following theoretical results. Toya [39] has shown by first principles of quantum mechanics that hydrogen adatoms

exist in r- and 5-states and that the hydrogen

adsorbed first on nickel exists predominantly in

the r-state, adatoms in the 5-state increasing with

further increase of the adsorbed amount. The.

r-state is that of adatoms in the usual sense, whereas

5 The critical complex is the system of a step, i.e., the set of particles involved in the step, at a particular configuration with its representative point on the critical surface. The critical surface partitions the configuration space appropriate to the

initial system of the step from that to the final system and is situated so as to minimize

the rate of transit of representative points of the relevant canonical ensemble in either direction; the initial or final system is the same set of particles at the state before or

after the occurrence of the step, respectively. The critical complex includes as its special case the activated complex as defined by Eyring et al. [H. Eyring, J. Chem.

Phys. 3, 107 (1935); W. F. K. Wynne-Jones and H. Eyring, ibid. 3, 492 (1935); M. C. Evans and M. Polanyi, Trans. Faraday Soc. 31, 875 (1935); 33, 448 (1937); M. Polanyi,

J. Chem. Soc. 629 (1937)] with special reference to the saddle point of the potential energy of the system of the step. In cases where there exist interactions between

systems of the step and other particles, the appropriate configuration space and the relevant canonical ensemble should be those of the assembly comprising all the inter- acting species [cf. J. Horiuti and T. Nakamura, Advances in Catalysis 17, (1966), section II. A.].

Table 6. Catalytic activities in hydrogenation of ethylene, adsorption heats of light ethylene, — AHE , adsorption heat of light hydrogen, — AHh , and percent d -character of metals [6, 14\

K is the ratio between the value of ki, = Vh/PH at 0 °C of a given metal catalyst and that of Rh.

Rh Pd Pt Ni Fe W Cr Ta

logio h 0 -0.8 -1.65 -2.6 -3.0 -4.0 -4.2 -4.4 — AHe kcal/mole 50 58 68 102 102 138 — AHh kcal/mole 26 27 28 29-32 32-36 45-52 45 45 % (/-character 50 46 44 40 39.7 43 39 39

9
Figure 4. Catalytic activity, A., of evaporated metal films and

the properties of the metals [ 14]. Films were evaporated in high vacuum and in case of Ni, in 1 mm Hg N2 as well on

glass wall kept at —183 °C; “Random” and “110” refer to the random orientation of

crystallites and a preferred orientation of (1 10)-lattice planes parallel to the basic

wall, respectively, as observed by electron diffraction of the Ni film evaporated in high vacuum or in 1 mm Hg N2 . A. is the ratio between the first order rate at 0 °C with respect

to hydrogen pressure per unit BET area of a given metal and that of Rh.

the 5-state is that of H atoms dissolved in the metal

but retained between the electronic surface of metal

and a plane through the centers of the metal atoms

in the first layer. Observed variations of electric

resistance [40] and work function [41, 42] with

amount of hydrogen adsorbed have been adequately

explained on this basis, and it was inferred that [43]

the r-state on tungsten is of an extremely low

energy so that the 5-state does not practically exist on tungsten, that hydrogen is irreversively adsorbed [44], and that hydrocarbons are stripped of

hydrogen atoms to leave carbon deposit on tungsten.

Methane will thus diminish the number of sites of

the critical complex as in 3.1.6.

It would be of some interest to decide whether

adatoms of r- or 5-state partake in the hydrogenation

reaction. Takeuchi and Asano [45] allowed nickel

oxide reduced at 200 °C to adsorb one after the other

small quantities of tritium and protium. Then, ethyl- ene was admitted over the catalyst. The ethane thus

formed was found less radioactive when protium

Figure 5. Linear relation between log\o A and valency ( Pauling) X percent d -character [35].

K is the ratio between the first order rate at 0 °C with respect to hydrogen pressure per unit BET area of a given metal and that of Rh: cf. Beeck [14].

was admitted first: hence, that decided which the

initially adsorbed hydrogen was active in hydrogenation. It would follow from this experimental

result, with reference to Toya’s theory, that only

hydrogens in the r-state were catalytically active.

Since nickel might not, however, be sufficiently

reduced and evacuated at 200 °C, it is desirable to confirm the result with nickel reduced and evacuated at higher temperature or with a clean surface

of evaporated nickel film.

3.2. The close correlation of the catalytic activity

with properties, of metals as seen in figures 4(a)

and 4(b) would suggest an investigation of alloys

whose properties vary continuously with composition. The theory of catalysis of Dowden [46] predicts,

in particular, that Ni alloyed with more than 60 percent Cu has its Wholes filled by electrons from Cu

and is deprived of its catalytic activity. A lively

interest has been aroused by this state of affairs

in the catalytic activity of alloys for ethylene hydrogenation which has, however, been earlier explored

by Rienacker and his co-workers [47-51].

3.2.1. Rienacker’s work provides the following

information.

10
3.2.

1.1. Alloys of transition elements with Cu, i.e., Ni-Cu [47], Pd-Cu [48], and Pt-Cu [48, 50], were

prepared in the form of thin plates, which by means

of x-ray analysis were confirmed to be disordered

when flashed or flashed and quenched but ordered

with a superlattice when alloys of the appropriate

atomic ratio were annealed. In their experiments

runs were conducted by allowing an equimolar

mixture of ethylene and hydrogen of 1 atm total

pressure to flow through a catalyst bed and by

analyzing the effluent gas for the ethane-yield; the

absence of methane in the effluent gas was therewithal confirmed. The results are shown in figure 6

in comparison with the extent of parahydrogen

conversion effected by the same catalysts. The

following comments are remarked [50, 51, 48].

The activity of these alloys in catalyzing the hydrogenation increases, as seen from figure 6 with their

content of Ni, Pd, or Pt only up to a certain small

value of the content and the remains constant,

closely in parallel with their activity in catalyzing

parahydrogen conversion [50].

Figure 6. Activity of alloys in catalyzing the hydrogenation of

ethylene in comparison with that in catalyzing parahydrogen

conversion [57]. An equimolar mixture of C2 H.J and H2 was allowed to flow with a rate of 20 cm Vmin

and 50 cm length at 1 atm total pressure. The catalyst was conditioned at 650 to 800

°C in a flow of hydrogen for several dozens of hours before every run. The content of ethane in the effluent gas was determined, hence the percentage conversion. Para- hydrogen conversion was observed with the same catalysts statically at 235 mm Hg

hydrogen pressure by means of the thermal conductivity method.

Alloys with superlattice have lower activation

heats, although their activity is much the same as

that of disordered alloys [47, 48, 49].

3.2. 1.2. The catalytic activity of Cu-Ag alloy was

observed by Rienacker and Bommer [49] at 550 and

700 °C, but its dependence on composition was

found imperceptible.

3.2.2. Further data are provided on the dependence

of the activity of alloys on their composition.

3.2.2. 1. Kowaka [52] observed at 100 °C a pronounced activity of Ag-Pd alloys of Pd content above

40 atom percent in hydrogenation of ethylene but

practically none below 40 atom percent.

3. 2. 2. 2. Best and Russell [53] have observed the

activity of Cu-Ni alloys in catalyzing the hydrogenation of ethylene from —70 to above 100 °C;

the results indicate that the activity of the alloys

outweigh that of any pure component, in contrast

with the results at 500 °C shown in figure 6.

3. 2. 2. 3. Farnsworth et al. [54, 55], observed the

hydrogenation of ethylene over Cu-Ni alloy plates

subjected to bombardment with Ar+. Figure 7 shows

the results obtained at 40 °C in terms of the first order rate with respect to hydrogen pressure. The

activity of these alloys attained a maximum at a certain value of bombarding current, whereas such

is not the case with pure nickel. The figure shows

the maximum exaltation of activity at 60.5 percent

Cu content. Figure 8 shows the relative activity at 40 °C of catalyst plates bombarded and then

annealed at different temperatures. The activity of

pure nickel decreases gradually with increase of

annealing temperature, whereas the activity of

alloys keeps constant until the annealing temperature attains 400 °C, beyond which it decreases

steeply. Farnsworth et al. [54, 55], attributed the

latter, steep decrease to the migration of copper

atoms from inside the alloy to the part of surface,

which originally is rich in nickel and lattice defects

created by the bombardment.

Figure 7. Catalytic activity at 40 °C of Cu-Ni alloys bombarded with Ar+ ion versus bombarding current [54].

Catalytic activity is given in terms of first order rate with respect to hydrogen pressure. Alloy plates were preliminarily evacuated to 10~ 8 mm Hg at 900 °C.

273-052 0 - 68 -3 11
Figure 8. Effect of Ar+ ion bombardment and subsequent an- nealing on the catalytic activity of Cu-Ni alloy in hydrogenation of ethylene [54].

Activity ratio is the value of the catalytic activity at 40 °C of plates of the alloy bombarded with Ar+ and subsequently annealed, divided by that of the same plates similarly bombarded but not annealed. The catalysts were pretreated similarly to those

of figure 7 and bombarded with 120 fiA current at 500 V for 10 min.

3.3. Important contributions have recently been

made by application of the microcatalytic method

[56] developed by Emmett’s school to the studies

of promotion and poisoning effects of preadsorbed

hydrogen on the hydrogenation of ethylene, parahydrogen conversion and 1 H2-D2 equilibration over Cu-Ni alloy catalysts. In the microcatalytic

method, helium is allowed to flow, as a carrier,

through a differential reactor packed with 5 cm3 catalyst which is directly connected with a gas

chromatograph. A slug of reactant gas mixture,

60 percent H2 + 40 percent C2 H4 , was passed over

the catalyst and then directly through the chromatographic column.

3.3.1. Hall et al. [57, 58, 59], observed the above

mentioned reaction at 200 °K with the catalysts

pretreated in two ways, i.e., “H2 -treated” and

“He-treated,” with a view to find the expected effect

of preadsorbed hydrogen diminished in case of

“He-treated,” as compared with that of “H2

- treated.” The catalysts were reduced in a flow of

hydrogen overnight at 350 °C and, in case of “H2

- treated,” cooled in the same flow down to the reaction temperature or, in case of “He-treated,” kept

in a flow of helium at 350 °C for 30 to 45 min and

then cooled in the same flow of helium down to the

reaction temperature. Figure 9 shows the catalytic

activity of the alloys against their composition; the

“H2 -treated” catalyst is more active for hydrogenation of ethylene than the “He-treated” one

except for pure nickel, where the reverse is the

case. Hall and Emmett [58] thus found that the

conversion (i.e., formation of ethane) over pure

nickel was increased from 50 percent for “H2

- treated” t<3 95 percent for “He-treated.” “H2

- treated” copper was found 12 times as active as the “He-treated’ one. Figure 9 shows the results

of Hall and Emmett [58] side by side with the new

results of Hall and Hassel [57].

FIGURE 9. Catalytic activity of Cu-Ni alloys in hydrogenation

of ethylene at 200 °C [57, 58].

O: Hall and Emmett (1959) [58], O: Hall and Hassel (1963) [57].

The catalysts were reduced at 350 °C in a flow of hydrogen overnight and then, in case of “H2 -treated,” cooled in the same flow down to the reaction temperature, or. in case of "He-treated,” kept in a flow of helium at 350 °C for 30 to 45 min and then cooled in the same helium flow down to the reaction temperature. The catalytic activity

is given in terms of percent hydrogenation at 200 °K per m- BET area as observed by

passing a 8 cm3 NTP slug of 60 percent H2 + 40 percent C2 Hj in the helium carrier of 50 cm3/min flow rate.

The conversion over “He-treated” nickel was

reduced to 82 percent by passing slugs of the same

composition 16 times consecutively. In case of

Cu-Ni alloys, Hall and Emmett [58] found that the

conversion over “H2 -treated” (cf. legend of fig.

10) catalyst was unchanged by passing slugs re- peatedly, whereas that over the “He-treated” one

(cf. legend of fig. 10) thus gradually increased.

FIGURE 10. Effect of pretreatments on Cu-Ni alloy of 34.3 atom

percent Ni [58], Both in the first and the second experiment the catalyst was preliminarily He-treated

as described in 3.3.1. and slugs of 60 percent H2 + 40 percent C2 H, were passed over

the catalyst at —42.5 °C successively. After the third slug had passed over the catalyst

in the first experiment, the hydrogen stream was turned back over the catalyst at — 42.5 °C for 30 min, following which it was swept out with helium carrier gas and the

catalytic activity redetermined with the next three consecutive slugs. The catalyst was treated similarly after the sixth slug with purified ethylene and its effect was ob- served with the seventh and eighth slugs. In the second experiment the catalyst was kept in hydrogen flow at 350 °C for 30

min. (H.-treatment in the figure) after the third slug and kept in helium flow at 350 °C

(He-lreatment in the figure) after the fifth slug, respectively. The first and second ex- periment were conducted with the same charge of catalyst successively with the He-treatment described in 3.3.1 applied inbetween. Reproducible results were obtained

as shown in figure 9.

12
They hence concluded [58] that the poisoning

by absorbed complex referred to by Beeck [6, 14]

and Jenkins and Rideal [13] is a relatively minor as compared with that of preadsorbed hydrogen.

Hall and Emmett [58] found that the activity of

“He-treated” alloys in terms of log (% conversion

at 200 °K per m2

) increased monotonously with

the mean valency of metal atoms in the alloy ac- cording to the valence bond theory of Pauling [36] as well as with percent (/-character over the region

of its composition, where the catalytic activity varied

linearly with atom percent of nickel as seen from

the curve “He-treated” in figure 9. The activation heat of catalyzed hydrogenation

at temperatures around 200 °K was found [58],

irrespective whether “He-treated” or “H2 -treated,”

to be 8 kcal for pure Cu, ca. 5 kcal for a Cu-7.8

percent Ni alloy and 4 kcal for Cu-alloys of Ni

contents of 14.7 percent and above, including pure

nickel.

3.3.2. Hall and Hassel [57] observed in the case of

other catalysts the ratio between the activities of

“H2 -treated” and “He-treated” samples in the

hydrogenation of ethylene as below:

G-Fe-51 (pure iron catalyst from M. K. Research & Development Co., Pittsburgh,

Pa.) 0.1

G-Co-51 (cobalt oxide catalyst from the same

company as above) 0.4

P-2007 (singly promoted iron-synthetic am- monia catalyst containing 3 weight %

A12 03 , from U.S. Bureau of Mines) 0.4

89 EE (cobalt-thoria-magnesia-Kieselguhr catalyst of the composition 100 : 6 : 12 : 200 in

weight, from U.S. Bureau of Mines) > 1 and

Ni(0104) (nickel-kieselguhr catalyst containing 59 wt % Ni, from Harshaw Chem.

Co.) < 1 The “H2 -treated” catalysts are thus less active than

the “He-treated” ones with the exception of 89 EE.

3.3.3. Hall, Lutinski, and Hassel [59] have investigated comparatively the effects of an alternative

set of pretreatments, i.e., “outgassed” and “H2

- cooled,” on the catalytic activity in hydrogenation

of ethylene, parahydrogen conversion and ’H2 — D2 equilibration at 200 °K with Cu-Ni alloys. The catalysts were reduced at 350 °C for 2 hr, at 500 °C for

2 hr and then again at 350 °C for 12 hr. In the pretreatment “outgassed,” the reduction at 350 °C

overnight was followed by evacuation at the same

temperature and then by cooling down to the reaction temperature. The pretreatment “H2 -cooled”

is the “H2 -treated” one followed by an evacuation

at the reaction temperature for 30 min. The amount

of preadsorbed hydrogen is expected to be diminished in case of “outgassed” relative to that of

“H2 -cooled.” It was thus found that the activity

of “H2 -cooled” Cu-Ni alloys was two to three times

that of “outgassed” alloys uniformly for all three

reactions, while the reverse was again the case with

pure nickel.

It is remarkable that parahydrogen conversion

as well as 1 H2 —

D

2 equilibration over a Cu-Ni alloy

of 72.4 atom percent Ni is accelerated severalfold

by the preliminary passage of a slug of ethylene in

both cases of pretreatment, although the reactions

are retarded by coexistent ethylene. The activation

heat of parahydrogen conversion was found 4.2

kcal in either case of pretreatment, whereas the

preliminary passage of an ethylene slug reduced

it to 3.9 kcal for the “outgassed” and 3.0 kcal for

the “H2 -cooled” catalyst, respectively. The activation heat of ! H2 —

D

2 equilibration was 5 kcal in

either case of pretreatment.

3.4. Ru-Pt binary catalysts of 20-40 percent Ru content being not specified whether being alloyed or not, are known to exhibit an activity 2 ~ 6 times larger

than that of pure platinum [60] in catalyzing the

hydrogenation of such polar compounds as nitrobenzene, cyclohexanone, maleic acid, and methyl butynol, whereas no contribution appears to have been

made toward the study of its catalytic activity in

hydrogenation of ethylene.

4. Reaction Kinetics of Catalyzed Hydrogenation

The reaction kinetics of the catalyzed hydrogenation was extensively investigated over a variety

of simple metals as catalyst, whereas work on

alloys was limited so far to studies on the dependence of kinetic parameters, e.g., rate and

activation heat, upon the composition of alloys

under suitably selected conditions as reviewed in section 3. A detailed account of the reaction

kinetics is hence given next, with special reference

to catalysts of simple metals for hydrogenation of

ethylene.

4.1. The rate vn of the hydrogenation is determined

on the basis of the material balance in accordance

with the stoichiometric equation

C2 H4 + H2 -C2 H6 . (4.1)

The applicability of the material balance has been

verified by Rienacker and Bommer [47] at 596 °C

by a flow method. Miyahara, Teratani, and Tsumura [61] has shown mass-spectrometrically that

the equimolar gas mixture of reactants of 0.1 mm

initial total pressure over evaporated nickel film was converted exclusively to a mixture of ethylene,

hydrogen, and ethane. Miyahara [22] observed that

13
the total pressure of a 0.93:1 mixture of ethylene

and hydrogen decreased from its initial value

of 30.0 mm Hg ultimately down to 15.6 mm Hg

in a constant volume over evaporated nickel film

coincidently at 91, 114, and 129 °C, which verified

the conclusion from the material balance of eq (4.1)

that the final total pressure should be 30.0 mm Hg

X 1/(1 + 0.93) = 15.6 mm Hg. We have seen, on the

other hand, in section 2, that a small amount of

ethylene is subjected to dehydrogenated adsorption,

which may cause a deviation from the above material balance (cf. 2.E.1); it is inferred from these re- sults that the disturbing effects of the dehydrogenated adsorption are negligible for sufficient

amounts of reactant gases.

4.2. Table 7 shows the kinetic parameters of the

catalyzed hydrogenation in the presence of metallic

catalysts. The first row shows the kinetic parameters

of the uncatalyzed homogeneous hydrogenation in

gas as observed by Pease [62] for reference, which

ought to be excepted from the following illustration

of columns referring to the catalyzed heterogeneous

hydrogenation. Every blank indicates the lack of

relevant description in the original paper, whereas

“none” means that an appropriate process is not

applied according to the original paper.

The column I gives the isotopic specification of

the hydrogenation of ethylene, protium, deuterium

and their mixture which are denoted by *H, D, and

H, respectively, in accordance with the symbolism

noted in section l. 6 The column II indicates the species of metal

used as catalyst and the column III the form

(and/or condition) of the catalyst, i.e., powder,

foil, plate, wire, thimble, evaporated film or supported; when supported, the description is given,

e.g., as 1 percent on SiCX, indicating the weight

percent of the catalyst metal and the material of

supporter.

The column IV gives the procedures of preparation of the catalyst in order of their application.

The column V presents, in distinction from the

“preparation” in column IV, the pretreatment of

the catalyst for conditioning the catalyst in order

to secure reproducibility. “None” means that no such treatment is applied except the evacuation of

the product of the foregoing run, in cases where the

reaction is followed in a closed space as commented

upon below.

The column VI gives temperature and column

VII shows the initial values, PE ,o and PH ,o, of

partial pressures of C2H4 and H2, PE and PH , respectively.

The column VIII gives three points of specification of the “modes of measurement.” The first point specifies whether the “static,” “stir,” “circuation,” “thermal siphon,” “flow” or “flow-circulation” method of following the reaction was used.

6 Hydrogen atoms of approximately 99 percent D content is denoted by D, light hydrogen with natural D content by 'H, respectively, but hydrogen gas of intermediate D content is denoted by H in this table.

In the “static” or “stir” method, the reactant gas j mixture is kept statically or stirred by means of a

stirrer in a closed vessel over the catalyst, while in

“circulation” the reactant gas mixture is driven by

a circulation pump through a closed circuit over the

catalyst. In the “thermal siphon” method, the circu- ! lation is effected by thermal siphon instead by

means of a circulation pump. In the “flow” method,

the reactant gas mixture is allowed to pass through a

catalyst bed toward an open space. In the “flowcirculation” method, the gas mixture is rapidly

circulated over the catalyst through a circuit, which

is fed slowly with reactant gas mixture at one spot

while the circulating gas is led out from the opposite

spot of the circuit. The second point specifies that

“hydrogen” or “ethylene” is brought into contact

first with the catalyst, and the other reactant subsequently, or else that a homogeneous “mixture” of ! reactants is admitted over the catalyst. The third

point specifies the modes of following the rate law. ; In case of “static,” “stir,” “circulation,” or “thermal

siphon,” where the whole gas mixture is kept in a closed space, the rate law is determined either by i measuring the “initial” rate, i.e., the rate of reaction

at the moment of contact of reactant gas mixture

with the catalyst at different partial pressures of

reactant gases, or by following the “course” of the

reaction by decrease of reactants or increase of j products or both. In the former case, enough accu- racy of measurements and reproducible experimental conditions have to be secured, whereas in

the latter case it should be guaranteed that the course is not associated with such an advance of

poisoning that distorts the coherence of data. The

coincidence of the rate laws deduced by these

alternative methods is a necessary condition for

them being reality. The “initial” rate and the

“course” method with the whole gas mixture kept

in a closed space correspond, respectively, to the

differential rate measurement by means of differential reactor [111] and the analysis of integralconversion data [112] in case of the flow method,

which are denoted in the Table by “differential”

and “integral,” respectively. In the “flow-circulation” method the conditions of differential reactor

is secured by the rapid circulation.

The column IX shows the rate law, Vh^P'^P'^, of

the catalyzed hydrogenation in terms of m = d In Vh/d In PE and n = d In Vh/d In PH , where Vh is the

rate. Attached figures, if any, indicate the range

of application of the rate law. The column X gives

the optimum temperature referred to in section 1,

if observed at all.

In case of the “static,” “stir,” “circulation.” or “thermal siphon” methods, where the whole

gas mixture is confined in a closed space, Vh of

reaction (4.1) is determined, either by change of

the total pressure in the closed space or by the C2H6-

yield, whereas in case of the flow method the rate

is determined preferentially by C^H^-yield rather

than by the decrease of C2 H4 or H2.

14
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene.- Continued

The reactant ga» mixture was either confined in a close space over the catalyst or allowed to flow through a catalyst bed toward an open space. "Modes of measurement" in the respective

cases are as follows. L „ , ...

In the former case, the gas mixture was kept either "static or dynamic by stir with a stirrer, by thermal siphon.” or by “circulation" through a close circuit with a circulation pump,

respectively. “Mixture." "ethylene” und “hydrogen" mean that at the beginning of a run in the measurements, a homogeneous mixture of reactant gases, ethylene or hydrogen, respectively,

were first admitted into the closed space and allowed to contact with the catalyst. “Initial and “course refer to the mode of observing the kinetics of the reaction by measuring the initial

rate at different partial pressures of reactant gases or by following the change of composition of a charge of reactant gas mixture with time, respectively.

> extem!T"l,a“'he ubsereedrale'cM be direelU “femd . o".Vr«o. 11^ '? ,he <U«fcronUal method the ronvenfan llireugh the Mlalytt bed i» realricled In practically iltbnite.ini,.I of flow rates to analyze them for the rate as a function of the partial nrrosiir.*.* I prT** ur';* * n ,lu‘ ,nletlral metho.l finite changes in partiul pressures are observed .is functions

• • - P

,

pr^sures - •" *he flow circulation method a gas mixture reacting over a catalyst bed is rapidly circulated through « circuit. lure is constantly led out for analysis; the result* give directly coherent data of rale and partial pressures.

which is steadily supplied with reactants while the circulating n

I It III IV V VI VII VIII IX X XI XII

Reaction Metal Form Preparation Pretreatment

Reaction

temp. °C

Initial pressures of

ethylene {Py:, <>) an^ hydrogen (/Vo) mm Hg

Modes of measurement

Rate law

Optimum temp.

t\ °C(=FX °K — 273) Activation heat kcal mole

1 ft In vi, Authors

i> In Pt: ~ m

ft In vi, d In Pu ~ n Given by the authors

C.'H. + 'Ha

Homogeneous reaction 475 ~ 550

Rn. ii/P k. n= 1 . 2, 3

total pressure = 760,

380. 190

In Pyrex glass vessel 1 i 43.15 (62|

Ni

Foil

Nitrate formed

on the surface decomposed by

heating and

reduced in Hj

at 270 °C

Evac. to less than 0. 1 mm Hg

73 ~ 200

Ij

k. « = 30

Pa.,i = 730 Static, mixture, course

i 137 1.8 (F < Fx ) |63|

do 100 ~ 192 Py. (i = 730 Pn. o = 30

do 1 [63]

700 °C in H2 for 24 hr 400 ~ 600 Pe.« + Ph. o = 760

PE. 0 • P\\. 0—1*1 Flow, differential 5.0 ( 400 - 500 °C) [47]

Reduced at 200 °C - 10 - 130 l\ „ = 0.03 0.04

Static, ethylene, course

0 1 (F < T\)

1 1 (F>FX )

60 4.6 (7'< 7’x ) [64

1

Plate

Outgassed at 900 °C in ultra- high vacuum

35 ~ 85 P».a> PE. o = 0.02-21.7Static, hydrogen, course 0~- 1 i 120 (/’k = 2 — 4)

ll.0±0.3 (Ar

1 ion bombardment)

1 0. 7 ±0.2 (Outgassing and

annealing)

9.0 ±0.6 (Outgassing and

quenching)

7. 9±0.5 (Ar

1 ion bombard- ment and annealing) 6.0 + 0.4 (Contamination at elevated temp.)

|65|

600 °C in air and 300 °C in H>

300 °C in H,

for 20 hr

50 l\:. o = PH . o= 11.3 Circulation, mixture, course

0.8 (initial) 1.0 (final)

[66

1

Wire

600 °C in air and 330 °C in H->

200 °C in H-, 0-200 /'k. u = 1 - 5 Pu . o = 2-8 Static, mixture, course

ft In vi, _ ,,

ft In ( Py + P„ )

140 (/' k = 3. 7\,= 5) [67|

[2]

C2 'Hy + D, Ni Wire

5

do do do 160 (/\: = 3. I‘u = 5 ) 8

C,'H, + 'H, Ni Wire 600 °C in air and 300 °C in H2 20- 155 !\ (i = 7 - 20 PH . o = 10-30

Static, mixture, course

Co’H. + D, Ni Wire

600 °C in air and 330 °C in H2

None 70 - 207 TV. o = 20.5 - 113 PH . o = 82.4 -159

Static, ethylene, initial 0

(15

1 6 °C)

14 (70- 100 °C)

0--I (207 °C)

|68|

do 55 - 120 Static, ethylene, initial 0 1 8.2 + 0.5 [691

C2 'H,+ 'H, Ni Wire

600 °C in air. 300 °C in H-, and

annealed at 600 °C

300 °C in H-, -45 - 95

/V o = 0.02-0.15

P„. o = O.02-0.15

(initial

Static, mixture,

j(course

0

(-45 °

0.7

C. 0°C)

60

(/\: = 0.03. I’u — 0.09)

5.3 ±0.2 (F < 7’x) [70[

Red-heated in air and 360 °C in H-.

Outgassed at

at 200 °C

99 - 165 Pr . o=10 -130

/V„ =1°~ 160

Static, mixture, course W' _A|

1 + k-,Py

0 (= /<F

2

ft In k,l<iT) [71

1
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. Continued

I II III IV V VI VII VIII IX X XI

Xll

Reaction

temp. °C

Initial pressures of

ethylene (PE , 0 ) and

hydrogen (PH .o) mm Hg

Rate law Optimum temp.

t x °C(=TX °K — 273) Activation heat kcal • mole' 1 Reaction Metal Form Preparation Pretreatment Modes of measurement

*!"

o h In PE

r) In vi,

d In P„- n Given by the authors

Authors

Heated in air and in H2

300 °C in H2 0.5 hr

83 - 190 !\ ,,= 20 - 360

PH . o = 50 - 400

Static, initial 1.2 -0.5

(135

0.7 °C)

180

(PE =1.1, P„ = 3.7)

5

[72]

Wire

850- 1150 °C in

air, 300 - 420 °C

in H>

62 - 201

PE ,, = 380-3040

PH , „ = 380 — 6080

Stir, hydrogen, initial 0

(135-

0.97 ±0.07

188 °C)

13.4 (Porous, active) 15.5 (Reactivated by reduction)

1 1.3 (Smooth)

|73]

Ni(NO: ,) 2 decomposed at 400 °C

and 480 °C in H2

Evac. 2 hr -78-0

PE o= 100 -400

PH . o= 100 — 400

„ . [initial Static, mixture

j

(

, ourse -0.6 0.98

Vl cc v" (1 +kpH + k'pK )

2 6

[12, 74]

NiO reduced at 350 °C in H,

250 °C in H2 overnight

-78 - 125

PK , o = 25.3

/•’ll. „ = 507 Flow, differential 4

[58]

C2 'H, + 'Ha Ni Powder NiSi alloy

refluxed

(Raney Ni)

300 °C in H. 0 - 180

^k.0 + Ph. 0=50 -250 Thermal

. , mixture, course

siphon,

0.6

/Calculate by th< by the author fo

\

128

0.55

rate law given \

r pE = PH =100

°c j

v

oc

" (1 + kPH + k' PE )

// = 0.030. A' = 0.027\

\ 128 °C )

18.7 ± 1 (100 - 150 °C) 1751

Ni(N03 ) 2 decomposed

at 400 °C, 500 °C

in H. 10 hr and

350 - 500 °C in H2 15 hr

100 °C in H2

1 hr

53 - 123 PH, 0 IPE, 0 = 1.2

o + A

, h .«= 760

Flow, differential

8.1 153]

None -80-150 Circul. 0 1 10.7 161

Evaporated

film

190 °C in C2 H,

0.5 hr None 20 - 180

PE .o = 2~10

Ph .o = 2~ 10

Circul., mixture, initial 0

(114

1 °C) v" “ \ P

+kPE (165

°C)

165

( PK = PH = 50) 10.2 ( T< Tx ) [13]

190 °C in C,H,

0.5 hr

250 °C in H,

0.5 hr 0-96 Pe .o + Ph .o = 0.03 -300 Static, mixture, course 0 1 8.0 (PE + PH = 3)

[27]

C2 'H, + D2 Ni Evaporated

film None -120- -100 PE . o = 2.7 PH . o=8.1

Static, initial 0 0.5 7

[76]

None - 40 - 40 Pk. o = 49

Pn. o = 98 Static, mixture, course 0 1 9.1 - 10.3

[29]

Static, ethylene, initial -0.4(32.3 °C) — 0.2 (80 °C) 10.0 (Pe = 53, Ph = 55)

C.'H.+ 'H, Ni Evaporated

film

32.3 °C in 100 mm

Hg C2 Hj, 0.5 hr

32.3 °C in 100 mm

Hg H,, 0.25 hr

30 - 80 PE ,,= 10-300

PH . „ = 10 — 300

Static, mixture, initial Decreases with

PH from 1

to 0.7 7.8 (/'E = 48. PH = 58)

- [771

Static, mixture, course

Initially 0, then

2.3 and then 1 with decrease

of PE

(«= pH)

Decreases from

1 to 0.7 with

PH (« Pe)
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. - Continued

I II III IV V VI VII VIII IX X XI XII

Reaction Metal Form Preparation Pretreatment

Reaction

temp. °C

Initial pressures of ethylene (PE . «) and

hydrogen (PH .o) mm Hg

Modes of measurement

Rate law

Optimum temp.

t\ °C(=7’X °K — 273) Activation heat kcal • mole" 1 i> In vs _ Authors

f) In Py — m

d In tin

r) In PH _ ” Given by the authors

:,'H 4 +'H2

Ni

Evaporated

film

250 ~ 300 °C

in H2 40 min,

evac. at reaction temp. - 15 ~ 15

Ph. tIPE. I,= 1 PE . n+ Ph. ii = ~ 1-5

Static, mixture 6-8 178]

335 °C in H,

1.5 hr

-28.5-70 P, ,,= 10-300

PH- o = 10 ~ 300

Static, mixture, initial -0.5

(0

0.9

’C)

7(/>e = />h = 45)

|791

None 0 ~ 200 PE, 0 = 15

PH , o= 15

Circul., mixture, initial 130 •5.6 (T<TX ) -9.5 (7’> 7’x)

[22]

do -45 - 200 PE o= — 0.05

PH ,o=~ 0.05

Static, mixture, initial 35 5 {T< Tx ) 161)

do -40-220 PE .„ = 0.03~ 100

PH o = 0.03 - 20

Circul.] ....

Static |

mlxture< 7\ =

5300

< 14 -5->og l\.)

3.3 ~ 5.5 (T < 7’x) -5 14 {T> 7’x)

[80]

Supported

2.94%

on Si02

500 °C in H2 -78-0

Circul., mixture, initial

-0.08 ±0.12

(— 4(

0.67 ±0.10

°C)

8.4 ±0.5 [81|

Supported

on A1,0:)

Ni(NO:l ) 2 calcined

at 400 °C 10 hr,

reduced in H2 250 °C 24 hr,

170 °C in

H-> + excess C2 Hj

None 32-80

PE o=137~ 2090

PH> o = 326 — 3260

o.40 -0.90

'E,0'I H. 0

Flow, differential 0.33

(90

0.93

°C)

1 1.6(Pk = 550, P„ = 200) [82, 83]

Ni(NO,i)2 calcined,

700 °C in H2 2 hr

Oxidized in air reduced at 500 °C 2 hr

80 - 140 Pe.o+Ph. ..= 760 Flow, differential 8.2 [84]

Platinized

foil None 0-236

Pe ,„ = 20 — 111

PH .o = 20~67

Static, mixture

initial <0

(25

>0

°C)

160 (Pe = 40. P„ = 20) 10 (0-78 °C)

[85] course

d In Vh/d In (/

jk + Ph) = 1

200 °C in H.

12 hr 0-52 PE , „= 50 — 150

PH .„ = 50~ 150

Static, ethylene initial -0.5

(0

1.2 °C)

[86]

Pt Foil 650 °C in Ho

12 hr

70 - 130 Pe, »—

h, 0 = 380 Flow, differential 4.5 [48]

Wire

400 °C in air 20 ~ 30 min,

400 °C in H.

20 ~ 30 min,

200 °C in C,H,

30 min

300 °C in Ho

30 min

Pk. o = 20 — 80

Vo = 20- 100

Circul., mixture, initial

-0.5

(T<

0

(T>

1.2 rx

) i Px)

240

(PK = 26, P„= 116) 10 (T< 7'x ) [87]
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. Continue

I II III IV V VI VII VIII IX X XI XII

Reaction Initial pressures of

Rate law Optimum temp.

<x °C(=7’x °K — 273) Activation heat kcal • mole

-1 Authors Reaction Metal Form Preparation Pretreatment temp. °C ethylene (PE , n ) and

hydrogen (PH .o) mm Hg

Modes of measurement

<) In t>,, _

d In PE m

r) In Vi, __

FhTT^

Given by the authors

Cj, Hi+ 'H2 Pt

Supported

1% on

Al2 0:,

H.PtCli! heated

in vac. at 200 °C

and reduced in H, at 200 °C

12 hr

Reduction for shorter time

than in “preparation,” as activity decayed

-18-52

PE , o = 50 -200

P„. ,, = 20 — 200

Static, ethylene, initial

-0.5

(O'

1.2

C)

9.9 ±0.5 (0-50 °C) [88]

C2 'H., + D2 Pt -18-52

PE .„=50~ 200 -0.5 1.2 10.9±0.5 (0-50 °C)

PH o=20~ 200 (O' C)

C2 'H., + D2 Pt Supported

on AI2 O3

H2 PtCl« reduced

in H2 at 400 °C,

exposed to air

at room temp.,

200 °C in H2 0.5 hr

-20-50

PE ,o = 100 — 250 — 0.3 ±0.1 1 .0 ± 0.

1

15 ±2 (0 — 40 °C)

[89]

PH .o = SO~ 100 (0‘ C) (PE = PH =100)

Supported

1% on Si02

H2 PtCI„ heated

in vac. at 200 °C.

Reduction for shorter time

PE . o= 100 — 250 -0.5 1.2

reduced in H2 at 200 °C 12 hr

than in "preparation,” as activity decayed0-52 /

jh.„=50~ 100 (0‘ C) [881

Supported

on Si02

“Davison" gel

impregnated with

HjPtClfi

Circul., mixture, initial

0.25 ±0.07

(-4C

0.77 ±0.07

°C)

8.4± 0.4 [81]

Pt

Supported

0.05% on, Si02

H2 PtClfi calcined

at 538 °C in air

1 hr, reduced

in H2 at 500 °C

3 hr

10 min in Ho-flow at reaction temp.

45-93

PE , o=5.3~302

PH .o= 11.4 -760

Flow, differential

0

(97°, 45 C)

0.5

(77°, 45 °C)

16

(PE = 22.8, PH = 152)

[90]

C2 'H,+ 'H.

Supported

1% on Si02 -

A12 0;i

H2 PtCI„ reduced

in Ho at 400 °C,

exposed to air

at room temp.,

200 °C in Ho

0.5 hr

Reduction for shorter time

than in "preparation,” as activity decayed

0-78

PE , „ = 50 — 290

PH . o=50~ 160

Static, ethylene, initial -0.5

(O'

1.2

C)

[88]

Supported

1% on

HoPtCl« reduced

in Ho at 400 °C,

exposed to air

at room temp.,

200 °C in Ho

0.5 hr

- 18 - 50

PE .o=20~ 150

Static, ethylene, initial

-0.5 1.2

pumice [88] PH . o = 20 — 100 (0‘ C)

Pd

Plate

300° ~ 380 °C

in air, 250

°C in H2 8 hr

0-209

PE .n= 100 — 500

PH , o= 100 — 500

Flow-circulation

0

0.5

(22

(176

1 °C)

1 °C)

10.6 (0-42 °C)

1.2 (102-209 °C)

[91]

Foil

400 °C in air 20 ~ 30 min,

400 °C in Ho

20 — 30 min,

200 °C in C .H , 30 min

300 °C in H2 30 min

100 - 300

Pe. o — 20 ~ 80

P„,o=20~ 100

Circul., hydrogen, initial 0

T<TX

1r>7’x

230

(PE = 2.6, P„ = 1 1 7

)

[87]
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. — Continued

I II III IV V VI VII VIII IX X XI XII

Metal

Reaction Initial pressures of ethylene (PE .„) and

hydrogen (P„, (l ) mm Hg

Rate law

Optimum temp.

'x °C(=7'X °K — 273) Reaction Form Preparation Pretreatment temp. °C Modes of measurement

i) In Vh a In l\~ mft 111 Vh

i) In PH ~ n Given by the authors

Activation heat kcal • mole*

1 Authors

650 °C in H2 12 hr

70 ~ 130 Pe, » = Ph, 0 = 380 Flow, differential 10-14 [48]

Foil Annealed at 800

°C 2 hrs in

400 °C in H2

1 min 0- 180

pK . 0= 100

Ph.o — 100

Static, mixture, course 1 5.3 - 5.8 [52]

vac.

Thimble

Evac. 1 hr

at 350 °C 0 — 98

PE .o=100

PH . o=100

Stir, hydrogen, course 0 1 5.1 (Pure Pd)

6.1 (H2 treated)

7.3 (C2 H.i treated)

[92]

C2 'R,-I- 'H2 Pd Powder

PdCl2 reduced

with KOH and

HCHOaq.

200 °C in 02

200 °C in H2

70 - 120

PK ,«— 1-7 — 11.0

PH . o = 0.9 -6.4

«

Static, hydrogen, initial

1

(a-p

1

tase)

-2.9 [93]

200 °C in 0>

75 - 105

/' E , o = 49.2 — 151.0

do

-2.4 -—

Vh CC^ e

aPE/(PE+Pn)

• H

11.4 [93] 200 °C in H2 Ph.o= 199 — 560 (j8-phas e, 75 °C)

Supported

on Si02

“Davison” gel

impregnated with

PdCl2

Circul., mixture, initial

-0.03 ±0.07

(-3

0.66 ±0.55

0°C)

8.4 ±0.4 [81]

Supported

on A12 02

Reduced from a convenient salt

in H2 at 400 °C,

exposed to air at room temp., 200

°C in H2 0.5 hr

-36 - 77

Pe ,o = 25 — 200

PH , 0 = 25 — 350

Static, ethylene, initial

0

(-1

1

B °C)

11.4 ± 1.0 (50- 77 °C)

(PE = /'11 = 100)

194]

(VH^ + Do Rh

Evaporated

film PE . o = 2.7Static, initial 7 [761 None — IzO 100

PH . 0 = 8.1

C.'H^+'H. Rh

Supported

on Si02

“Davison” gel

impregnated with

RhCl.i • 3H2 0

Circul., mixture, initial — 0.74±0.18

(-7

0.85 ±0.11

6 °C)

[81]

C2 'H, + D2 Rh Supported

on A12 03

Reduced from a convenient salt

in H2 at 400 °C, -18-110

Pe ,o=30~ 100

Static, ethylene, initial

0 1 12 ± 2 (73 ~ 110 °C)

(PE = P„= 100)

[94]

exposed to air at room temp., 200

°C in H2 0.5 hr

Ph ,o=26 — 250 (79 °C)

CVH4 + D0 Ru

Supported RuC13 3H.0

0-80

PE .o=28~ 100 -0.2 1 8.7 ±0.5 (32 — 80 °C )

(PE = 75, P„ = 76)

[95]

ai2 o3 at 200 °C 5 hr Ph.o=54~ 165 (54 °C)
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. — Continued

I II III IV V VI VII VIII IX X XI XII

Reaction Metal Form Preparation Pretreatment

Reaction

temp. °C

Initial pressures of ethylene (Pk.<») and

hydrogen (PM . 0 ) mm Hg

Modes of measurement

Rate law Optimum temp.

f x °C(=7’x °K — 273) Activation heat kcal • mole'

1 Authors

/) In vi,

it In Py ~ m

i> In vi, a In P,, - " Given by the authors

C,'H,+ 'H,

Ru

Supported

on SiOa

“Davison” gel

impregnated with RuCla • 3HaO

Circul., mixture, initial -0.95 ±0.08

(-70

0.95 ±0.05

°C)

8.4 ±0.4 |81]

Ir Supported

on AlaO.i

Ammonium

chlorciridate reduced in H> at 400 °C, exposed

to air, 200 °C in Ha 0.5 hr

— 20 ~ 150

Static, ethylene, initial — 0.4 ±0.1

(60

1.6 ±0.1

5C)

13. 8± 1.0 (80- 120 °C)

(PK = 50, P„=100)

[89]

C2 'H.i + D2 Os

Supported

5% on

AlaO;,

Ammonium

chloroosmate

reduced in Ha

at 200 °C 5 hr

0 — 80 PE . o = 50

P„.„ = 27~203

Static, ethylene, initial (24

1

5 C)

8.5 ±0.5 (17-47 °C)

(Pe = Ph = 50)

[95]

Ca'Hj + 'Ha Cu

Foil

700 °C in H > 24 hr 550 ~ 700 PE .o+P„.„=760

Pe. o = 76 -380 Flow, differential

19.5 [47]

Evaporated

film

250 ~ 300 °C in Ha 40 min,

evac. at reaction temp.

PH.tl/PE.(l = 1

PE .o + PH . o~l-5

Static, mixture, course 0 0.4 6-8 [78]

Powder

Cu reduced and

annealed at 250 °C 1 hr150 ~ 275

Pe. o = 340 — 440

PHi o = 190 — 440

Stir

1 1

1

12.0 (150 - 200 °C)

1.3 (200 -250 °C)

0 (250 - 275 °C)

[96]

Cu reduced in H2 200 °C 30 ~ 40

hr, annealed at 450 °C 1.5 hr

0 ~ 20 PH . »/Pe.o = 0.5, 1.2

PE .o+PH , o = 380 -760

Static, mixture, initial

-0.4

(0°

0.8

C)

7.8 [97]

CuO reduced in H>

at 200 °C

30 ~ 40 hr, annealed at 500 ~ 550 °C

150 ~ 250 do

0.66

(200

0.8

°C)

10.8(150-200 °C)

7 (200 - 250 °C)

(Pe = 507 , P„ = 253)

[98]

CuCOa decomposed, reduced

in Ha at 350 °C

200 °C in Ha

overnight - 73 ~ 125

PE . o = 253

/Vo =507

Flow, differential 8 [58]

Cu(NO.i)a decomposed at 400 °C,

in Ha 500 °C

10 hr, in H.> 350 ~ 500 °C

15 hr

100 °C in Ho

1 hr -10-25

PH.o/PE, <> = 1-2

PE.0+ /

> H.o= 760

Flow, differential 7.9 [53]

Powder

mixed

with 50

mole %

MgO

CuO, MgO mixture reduced

in Ha at 250 °C

9-79 PE .o = 36 — 512

Pe. o + Ph. o= 760

Flow, integral 0 1 13.32 [99]
273-052

0

-

68

(Face

p.

14)

No.

Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. — Continued

. II III IV V VI VII VIII IX X XI XII

Reaction Metal Form Preparation Pretreatment

Reaction

temp. °C

Initial pressures of ethylene (/

JK .„) and

hydrogen (P„.„) mm Hg

Modes of measurement

Rate law

Optimum temp.

'x °C (=TX °K — 273) Activation heat kcal • mole

1 Authors rt In Vi,

it In l\. ~ m

it In Vi,

it In /'„ ~ " Given by the uthors

Ca'H^+'Ha Cu

Supported

on brick

Cu(NO:i)i decomposed at 200 °C

in Ha, annealed

at 500 °C 8 hr

0~ 100

f'i:. n = 95 — 570

l\\. « = 95 — 570

Static, mixture, initial

0

( 100

1

°C)

13.4 (not annealed 0 ~ 60 °C)

13.2 (annealed 60 100 °C)

(Pe = P„ = 380)

liooi

Supported

on glass

beads

Cuprous

hydroxides

reduced

194 ~ 220

/'k, ii = 253 — 507

P„,„ = 253 - 507

do 1

(22(

1

°C)

6 (

E = = 380) liooi

Supported

on SiOa

"Sorpsil" silica gel impregnated

with Cu(N03 ) 2

Circul.. mixture, initial

0.06±0.12

(80

0.69 ±0.09

°C)

8.4 ±0.4 181|

Supported

9.8% on

A1,0,

275 °C in H, 51 ~ 69

PE . o = 76 -532

PH , ,,= 152 -532

Circul., mixture, course " (i +kPE y

> 14.1 lion

Supported

on

kieselguhr

Cu(NO:,)2 reduced

at 300 °C in H2 109 ~ 258

PE . ,. = 46

/

jh. 0=113

Circul., mixture, course (T <

1 (T>

0.5 Tx )

0 Tx )

- 200 11021

Ca'H^+'Ha

CaD^+'H,

Cu

Powder

mixed

with MgO

4 : 1 mixture of Mg(OH)a,

Cu(OH)a reduced

-20-40

Pe ,» = 50~ 100

PH .o — 50 — 100

Static, mixture, course

1 1.8 (C.'H.)

11.3 (CaDj)

(Py = P» = 50)

1 103

C,'H4 + D2 Fe

Evaporated

film None -120- -100

PE . » = 2.1

PH . o = 8.1

Static, initial 7 [76|

Face

p.

14)

No.

7

n 33 + X Fe Evaporated

film

32.3 °C in C.'H4 0.5 hr

32.3 °C in Ha 15 min

30-80 Pe .»=10~300

/

jh.o= 10 — 300

Static, ethylene

initial

-0.6

(32.:

0.87

°C)

7.3(Pe = 55, /*„ = 52

)•

course

Decrease from

0.85 to 0.19 as PK increases

(32.:

0.84

i°C)

|77)

Static, hydrogen, course 0.94

| (32.3 °C)

Powder

Fe(Il) oxalate

reduced, sin- tered in vac.

Evac. at 360 °C

2 hr 0 - 175 Static

8.4 (30 ~ 75 °C)

1104)

s C2 'H, + D2 0

Fe Powder do do do do

8.3 (30 ~ 50 °C)

12.5 (55 - 75 °C)

Ca'Hj + 'H. Fe

Powder.

0.15%

AljO.i as impurity

425 - 450 °C in H2 60 hr and 525 °C

8 hr

450 °C in Ha 1 hr, evac. 2 hr -89 --40

PE ,«=80 — 585

PH ,o= 110 — 335

Static, mixture, course

0

(— 7<

1 -0.5

>°C)

5.1

(- 89 - - 79 °C. PK = P„ = 240)

[105]
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. — Continued

I II III IV V VI VII VIII IX X XI

XII

Authors

1105]

Reaction Metal Form Preparation Pretreatment

Reaction

temp. °C

Initial pressures of ethylene (PE .o) and

hydrogen (PH .o) mm Hg

Modes of measurement

Rate law Optimum temp,

tx °C(= Tx °K — 273) Activation heat kcal • mole

-1

it In Vi, d In PK ~ m

d In Vi,

i) In /'„ ” Given by the authors

C2 'H,+ 'H2 Fe

Powder,

1.59%K,0

1.3% Al2 0,

450 ~ 500 °C in H,

80 hr

450 °C in H2 ] hr evac. 2 hr — 89 40 ^.0 + ^1.0 = 450 Static, mixture, course 5.3( — 50 40 °C)

Powder,

0.15%

A12 03 as impurity

Fe oxide reduced

at 400 ~ 440 °C

59 hr and 515 ~ 532 °C 8 hr

in H2

400 °C in Hl

>

1 hr — 50 20

PE o= 100 — 400

Ph .„ = 50~300

Circul., mixture

initial (-35

0.6 °C)

4.2(PE — Ph = 200)

[106] course —

(-35

1.0

°C)

Supported

on brick

Fe nitrate calcined at 350 ~ 400 °C, reduced

in H2 at 450 °C,

sintered at 500 °C

0-20

PE> o = 253 — 507

PHi o = 253 — 507

Static, mixture, initial -0

(0

°

>0

C)

6.2(PE =PH = 380) [1071

Supported

on Si02

“Sorpsil” impregnated with

Fe(NO:,)a

Circul., mixture, initial

0.04 + 0.13

(30

0.91 + 0.11

°C)

8. 4 + 0.

[81]

Co

Supported

on SiO_.

“Sorpsil” impregnated with

Co(NO;|)2

do

-0.19 + 0.10

(-60

0.55 + 0.66

°C)

8. 4 + 0.

[81]

C2 'H4+D2 W

Kvaporated

film

None -120- -100

Pe,o = 2.7

PH . 0 =8.1

Static, initial 5-6 [76]

Ca'Hj + 'H-2

Ag

Foil 700 °C in H2 24 hr 550 - 700

Pe.o+Ph. o=760

PH .o= 103 — 388

Flow, differential 27.1 [49]

Supported

on brick

AgNOn calcined

at 350 ~ 400 °C,

150-250 °C

in H-2

50- 100

PE , o = 253 — 507

PH . o=253 — 507

Static, mixture, initial

0

(100

1

°C)

9.8 (PE = P„ = 380) [107]

Cu-Ni

alloy

700 °C in H,

24 hr

400 - 600

^e.o + Ph. o=760

PE ,o= 114 — 395

Flow, differential 2.5 (max. at ca. 50 atom % Ni)

(47]

Outgassed in ultra high vacuum

at 900 °C

Ar+ bombardment

35-85

PH. »>PE. 0

^e. o = 0.02 ~ 21.7

Static, mixture, initial 11 [65]

Evaporated

film

Evaporated from

Cu and Ni wires,

annealed in H2 at 300 °C overnight

250 - 300 °C in H2 40 min - 15 - 15Ph. «/Pe. o = 1

PE. “h P\\, 0 = 1*5

Static, mixture, course

0

(74.2 c

0.4

Vc Ni)

6-8 [78]

Evaporated

film 54.6 atom

% Cu

Evaporated from

alloy pellet

350 °C in H2 1.5 hr

-28.5-70

PE . 0=10 -300

PH . 0=10 -300

Static, mixture, initial -0.3

(0

°

0.9

C)

8.9 (PE = Ph = 45

[79|
Table 7. Reaction kinetics of catalyzed hydrogenation of ethylene. — Continued

I 11 HI IV V VI VII VIII IX X XI XII

Reaction Metal Form Preparation Pretreatment

Reaction

temp. °C

Initial pressures of

ethylene (/Vo) and

hydrogen (/Vo) mm Hg

Modes of measurement

Rate law

Optimum temp.

/x °C(=TX °K — 273) Activation heat kcal • mole”

1 Authors r) In vi, h In l\.~ m

d In vi, d In PM ~" Given by the authors

:2 'H4 +'H,

Cu-Ni

alloy Powder

Carbonates decomposed, red. in H-<

at 350 °C

250 °C in H2 overnight - 73 ~ 125

PH. 0IPE,o= 1.5

/

>K.o+/Vo= 760 Flow, differential 4 178]

Nitrates decomposed at 400 °C,

in H, 500 °C 10

hr, in H350 ~ 500 °C

15 hr

100 °C in H,

1 hr -75-41

^H. »IPK. o = 1 .2 ^E. o+PH . 0=760 Flow, differential

9.3 (- 70 - - 41

8C, 90 % Cu ) 9.7 (-75 63 °C. 63 % Cu)

153]

Ni-Fe

alloy

Evaporated

film

Evaporated from

alloy pellet of

10.8 atom % Fe

350 °C in H2 1.5 hr

-28.5-70 PK . 0 = 10 — 300

PH . o=10 -300 Static, mixture, initial -0.3 0.8

(0°C)

8.9 [79]

Ni-Pd

alloy

Evaporated

film

Evaporated from

alloy pellet of

5.5 atom % Pd

do do -0.2 0.6

(-28.5 °C)

7 [79]

Cu-Ag

alloy

Wire 700 °C in H-. 24 hr

550 - 700

ll

+

L\ Flow, differential 17- 16 (3-92 % Ag) [47]

Cu-Pt

alloy

Foil 650 °C in H,

12 hr

70- 130 PH. JPK . I* — 1 PE . 0 PH . o = 760

Flow, differential 5.4 - 14 [48]

Cu-Pd

alloy

Foil do do do

10 - 14 1 48]

Pd-Ag

alloy

Foil Annealed at 800 °C

2 hr in vac.

400 °C in H2

1 min

0 - 400 I\ (,= 100

PH .0= 100

Static, mixture, course - 5.2 (20 - 50 % Ag)

8 (60 % Ag)

|52]

NaH Lump Evac. at 200 °C

2 hr

100 - 200 /

>e,o=Ph .o=300 Static, mixture

8 [108]

LiH Lump do do

17 |108]

Ta

hydride Powder Evac. at 800 °C 200 - 500 l\ ,, = 50- 500

/V ,, = 50-500

Static, hydrogen, initial 1

(250 °C an

From positive

to negative as PH increases

d 300 °C)

<()(/'„ < 80, 250- 300 °C) > 0 (/’„ > 80, 250-300 °C)

|109]

CaH, Powder Evac. at 450 °C

1 hr - 78 - 450

PE . ,,= 50- 500

P„.„ = 50~ 500

Static, mixture, initial

1 1

( l\ < 100. 0-50 °C)

0 1 (PE > 100.0-50 °C)

200

(/

j e = 41.6, P„ = 41.7)

1.4 (0-150 °C)

(Pk = 41.6. /

jh = 41.7) |U0|
—

. .

• “

-

» > 'b

til '

•

i

o

). 4 ,

'

.

'

' ‘

’
The catalyzed hydrogenation is throughout

approximately first order with respect to hydrogen

partial pressure, as seen from table 7, irrespective

of the catalyst metal, preparation and pretreatment, whereas the dependence of its rate upon

ethylene partial pressure varies considerably with

catalyst metal, etc. The linear relation between

In Vh and In PE is rather poor in many cases, hence

the values of m = d In vn/d In PE in the table are

just as much inaccurate.

4.3.

Detailed comments will be made below upon

the representative case of nickel.

4.3.1. Zur Strassen [64] has introduced hydrogen

over nickel wire environed preliminarily by ethylene

under its own vapor pressure (0.03 mm Hg) at liquid

air temperature, and observed the decrease of total

pressure, which was identified with rate vn of reaction (4.1). He thus found that the reaction was first order with respect to hydrogen throughout. The

quotient vn\P\\ was found to vary with partial pres- sure PE of ethylene as [64]

v/i/Ph ^ Pe! ( 1 T & Pe) ? (4.2)

where k! is a constant at constant temperature, decreasing rapidly with increase of temperature^ k'PE passing unity around the optimum temperature, so

that m = d In Vh/d In PE is zero or unity sufficiently

below or above the optimum temperature, respectively.

4.3.2. In the above experiment of zur Strassen [64],

the catalyst was initially contacted with ethylene

as denoted by “.ethylene” in column VIII of table

7. Masuda [70] recently observed the hydrogenation

rate in the presence of nickel wire over approximately the same ranges of partial pressures, introducing a homogeneous mixture of reactant gases

over the catalyst. The reproducibility of catalytic

activity was secured within 15 percent by a pretreatment at 300 °C in hydrogen of 15 to 20 mm Hg

pressure for 1 hr followed by evacuation to 10-6 mm Hg. The initial rate was thus found proportional

to PEPii

7 from —45 to 0 °C. Figure 11(a) shows the

dependence of the initial rate on PH . It follows that

Ph3 decreases linearly with time, provided the above

rate law holds throughout the course of catalyzed

hydrogenation, which is verified as shown in figure

11(b), fulfilling the necessary condition, referred

to in 4.2., of the real rate law.

4.3.3. We see from table 7 that m = 0 and n = 1 at temperatures below the optimum, while m = n = 1 above the optimum in most cases, in accordance

with eq (4.2). However, Vh depends perceptibly

upon PE even at temperatures appreciably below

the optimum in those cases where the total pressure

of the catalyzed hydrogenation is higher than 1 atm [82], where the catalyst is preliminarily treated

with ethylene of much higher pressure [82, 101]

than in the case of the experiment of zur Strassen

Figure 11a. Dependence of the initial rate, vh , o, of hydrogenation over Ni wire upon PH .o [70],

Vh. o is the initial value of Vh given in hydrogenated percent C2H4 min-1 at PE = 0.049 mm Hg.

TIME , min

Figure lib. Partial pressure of hydrogen, PH (in mm Hg), in course of a run of catalyzed hydrogenation in the presence of

Ni wire [ 70]. O: 0 °C. O: 25 °C. O: 40 °C.

[64], and where the reaction vessel is preliminarily

only incompletely evacuated. Even a negative value

of m is reported [71, 74] with nickel powder, as shown in table 7. According to Schwab [113],

however, this negative value of m disappears when

the catalyst and the reactant gases are purified.

4.3.4.

Tucholski and Rideal [67] as well as Farkas,

Farkas and Rideal [2] reported that the catalyzed

hydrogenation in the presence of nickel was zeroth

order with respect to total pressure, whereas their

experimental results could be fitted adequately to the rate law with m — 0 and n = 1, the first order

rate (1 /t) In ( Ph.oJPh) remaining fairly constant as shown in table 8, where PH ,o is the initial value of

15
Table 8. Hydrogenation of light ethylene over Ni wire [2]

React. temp.

°C

Time t min

Partial pressures, mm Hg kh = (1/6 In (PH. oIPh)i min -1

Atom % of deuterium in hydrogen

Pe Ph

20 0 21.5 32.5 30.6

10 13.5 24.5 0.0123 30.0 25 5.5 16.5 .0118 33.2 37 1.0 12.0 .0127 33.8

155 0 20 24 62

9 13 17 22

155 0 13 16 0

? 10 13 13

4.3.5. The observations on activation heats are no

less divergent than the rate laws. Tuul and Farnsworth [65] have observed the catalyzed hydrogenation of ethylene in the presence of a 2.5 cm2 nickel

plate subjected preliminarily to different pretreatments. The results are, as shown in figure 12, that

the activation heat varies between 3.6 kcal and 12

kcal, revealing the so-called compensation effect.

The activation heat was derived from rate constants

kh at 35, 55, and 85 °C as deduced from experimental

results assuming the rate law, m = 0, n=l. The

linearity of In kh to l/T is, however, rather poor,

hence the activation heat is just as much inaccurate.

The cleanest surface is, according to them [65],

that bombarded by Ar+ ion, which reveals the highest activation heat, 12 kcal.

This high value activation heat coincides, however, with that on the carbided nickel surface

[13, 82, 114]. Moreover, Tull and Farnsworth’s observation of the optimum temperature, Tx , in con- junction with partial pressure of ethylene, PE , falls into the characteristic correlation between Tx and

PE , referred to below, of the carbided surface. It is possible that adsorbed complex on the nickel plate,

which was used for every experiment as mentioned

above, is decomposed by the bombardment to form the carbided surface. On the basis of the arguments in section 2, the most adequate value of the

activation heat below the optimum is 5 to 6 kcal as obtained by Miyahara and others [22, 26, 61, 64,

70, 80] with equimolar mixtures of the reactant

gases over evaporated nickel film.

4.4. An optimum temperature is observed, as seen from table 7, not only for nickel catalyst but also for

platinum, palladium, iron, and copper catalysts.

Tuul and Farnsworth [65] advanced and empirical

relation, in case of nickel, between the optimum

temperature £X(°C) and PE

(in mm Hg) as fx =30

log 10PE + 105. Sato and Miyahara [80] found linear

relations between logioPE an<l the reciprocal of the

absolute temperature of the optimum, Tx ,to hold for

reduced nickel wire, freshly evaporated surfaces or carbided surfaces of nickel film, respectively as

FIGURE 12. Compensation effect in the catalyzed hydrogenation

of ethylene over a nickel plate subjected to different pretreat- ments [65].

shown in figure 13; the latter two surfaces have been

denoted by F and C, respectively, in 2.8.3. The

linear relation over surface F is analytically [80]

(PE in mm Hg)

1/Tx = (1/5300)(14.5 - log10PE). (4.3)

The optima observed by Tuul and Farnsworth [65]

fall on the linear relation over surface C observed

by Sato and Miyahara [80] as mentioned above.

4.5. Reference is made to the interesting work of

Apel’baum and Temkin [91] on the catalyzed

hydrogenation on palladium membrane. The apparatus used was separated into a hydrogen chamber, A, and a reaction chamber, B, by a 0.3 mm

thick palladium membrane, as shown in figure 14. The membrane had an area of 15.7 cm'2 on the side

of the reaction chamber. A mixture of hydrogen

and ethylene was circulated through the reaction

chamber by means of a circulation pump, C, at a rate of 2 liter/min through a circuit which was

steadily fed with reactant gas mixture at a rate of

25 cm3/min, while a corresponding amount of cir- culating gas was led out simultaneously. The reaction was followed by measuring the amount of

ethane in the gas led out. Apel’baum and Temkin

have thus investigated the kinetics of the catalyzed

hydrogenation, simultaneously following the

fugacity of adsorbed hydrogen on the side of reaction chamber, which was identified with the hydrogen pressure PA in the hydrogen chamber adjusted

16
Figure 13. Dependence of optimum temperature, Tx , on eth- ylene partial pressure, PE , in catalyzed hydrogenation of ethyl- ene in the presence of nickel [80].

O: Freshly evaporated surface, F, of evaporated film or pretreated foil. : Carbided surface, C, of evaporated film. A: Pretreated wire.

Figure 14. Apparatus for simultaneous observation of the cat- alyzed hydrogenation of ethylene over Pd and of the fugacity

of adsorbed hydrogen [91].

A: ^-chamber, B: reaction chamber, C: circulation pump, T: cold trap at —78 °C, M: Hg-manometer. Annexed figures refer to respective authors as

1: Jenkins and Rideal [13], 2: Rideal [63], 3: Tucholski and Rideal [67], 4: Miyahara

and Narumi [114], 5: Tuul and Farnsworth [65], 6: zur Strassen [64], 7: Miyahara

[80], 8: Sato and Miyahara [80].

Table 9. Catalyzed hydrogenation of ethylene over palladium,

with fugacity of adsorbed hydrogen followed simultaneously [91]

Vh,x=o‘- Hydrogenation raie, Vh, at x = 0. x: Diffusion rate of hydrogen through the Pd-membrane.

Tem.

°C

No. of

experi- ment

Partial pressure, mm Hg in reaction chamber

Fugacity of adsorbed

hydrogen,

PA mm Hg

Vh, x=0 C2 He cm3 NTP/hr c2 h4 c2 h6 h2

22 15 231 84.5 424 165 156

16 239.5 77.5 439 205 141

18 254.5 59.0 456 235 107 20 263.5 35.5 453 64 70

176 1 15 242 496 492 186

2 184 345 227 224 456

4 26 231 504 500 350

7 85 332 336 327 470

8 111 290.5 357.5 353 419

to zero diffusion rate of hydrogen through the membrane. The conditions of experiments and observed

kinetics are shown in table 7 and the associated

observations of PA-values in table 9. We see from table 9 that PH = PA at 176 °C but

Ph ^Pa at 22 °C, which shows that adsorbed hydrogen is in equilibrium with hydrogen in gas or adsorption and desorption are so much rapid at 176 °C but not at 22 °C.

Apel’baum and Temkin observed further the

rate Vh of hydrogenation in conjunction with the

rate x of diffusion of hydrogen through the membrane to find the increment in number of ethane

molecules per diffused hydrogen atom, i.e..

The result, n = 0.01 at 176 °C and n = 0.5 at 22 °C

indicates that the hydrogen used in the catalyzed

hydrogenation originates almost all from gaseous

hydrogen in the reaction chamber at 176 °C but

from diffused hydrogen at 22 °C in conformity with

the above conclusion on the adsorption.

5. Reactions Associated With the Catalyzed Hydrogenation

Farkas, Farkas, and Rideal [2] discovered that

the catalyzed hydrogenation of ethylene is accompanied by parahydrogen conversion and exchange

of hydrogen atoms when they followed the parahydrogen content and deuterium content in hydrogen by means of the thermal conductivity method.

Since 1950, relative amounts of different deuteroethylenes and deuteroethanes in the deuteration

product of ethylene have become traceable by means

of mass spectrometry. Infrared spectrometry has

17
also become popular in the analysis of deuterocompounds. The profiles thus disclosed of the

catalyzed hydrogenation impressed an unexpected

complexity of the problem on the one hand but

promised to be powerful tools of solving it on the

other hand.

5.1.

Experimental Methods

Such profiles of the reaction which are traceable

by means of the thermal conductivity gage alone

are dealt with in 5.1, and those extended by means

of mass and infrared spectrometry in 5.2.

5.1.1.

Farkas, Farkas, and Rideal [2] followed the

parahydrogen conversion or the deuterium atom

fraction in hydrogen in course of the hydrogenation

of ethylene at 20 °C in the presence of nickel wire

Figure 15. Parahydrogen conversion associated with catalyzed

hydrogenation of ethylene [2], Pe. o = 19 mm Hg, PH , o = 23 mm Hg, 20 °C.

preliminarily oxidized at 600 °C and reduced by

hydrogen at 300 °C, grew distinctly rapid as soon

as ethylene was exhausted by hydrogenation,

as seen in figure 15, (1) its rate being approximately equal to that in the absence of ethylene

[2]; (2) that the rate of parahydrogen conversion

at 20 °C of 25 mm Hg parahydrogen was unchanged

by admixture of 17 mm Hg ethane, (3) that the partial pressure of ethylene due to catalyzed hydrogenation decreased linearly with time at 20 °C

for the first 30 min as seen in figure 15, and (4) that

such a linear decrease was no longer observed

above 60 °C. By means of deuterohydrogen they [2] observed (5) that the deuterium content of hydrogen

at 20 °C remained nearly constant during the whole

course of hydrogenation, or it even increased

slightly, as seen in table 8 until ethylene was almost

exhausted, and (6) that at 155 °C the deuterium content in hydrogen decreased rapidly, in contrast

with (5), (see table 8) from 66 to 22 atom percent

while light hydrogen, by which the residual hydrogen was replaced, regained 13 percent deuterium from

the ethylene during just a slight progress of hydrogenation as seen in table 8. The exchange reaction is practically arrested at 22 °C but released at 155 °C as seen in results

(5) and (6). The slight increase in deuterium content

at 22 °C can be attributed to the isotopic effect on

the reaction rate, which enriches deuterium in

hydrogen.

5.1.2.

Twigg and Rideal [68] observed the cata- lyzed deuteration of light ethylene with equimolar

pure deuterium in the presence of the same nickel

catalyst as used by Farkas, Farkas, and Rideal [2] with special reference to the deuterium content of

hydrogen. Successive measurements of hydrogenation and exchange rate conducted without pretreatments were corrected for an appreciable decay of

catalytic activity by measuring the hydrogenation

rate at a fixed temperature and the partial pressures

of reactants just before every run; then, the hydrogenation rates and exchange rates measured were

multiplied by the correction factor n/r,,, where r\ and r„ are the hydrogenation rates observed at the

fixed conditions just before the first and the nth

run, respectively. Twigg and Rideal [68] observed, on the one hand, the initial rate of hydrogenation and the initial rate of hydrogen exchange

t'ex.H ~ dxft/ dt, at 156 °C at different partial pres- sures of reactants, finding that both reactions were

first and zeroth order with respect to hydrogen and

ethylene pressure, respectively. They followed, on

the other hand, the course of deuteration by determining the deuterium atom fraction, .x H , in hydrogen

and the nonequilibrium fraction, 1 — a, of hydrogen,

where u = ['HDJ/pHDJgq is the ratio between the

actual concentration, [

! HD], of ‘HD and the concentration [‘HD]eq which would result, were the

existent hydrogen equilibrated, i.e., brought to equilibrium with respect to the reaction, ‘H2 + D2 =2'HD. The nonequilibrium fraction 1 — a is plotted

against xH in figure 16. The activation heat of hydrogen exchange

RT~d In v ex , H/dT was found to be 18.6 kcal over

the range of temperatures from 84 to 100 °C, and

to decrease gradually with increase of temperature

down to 4 kcal at 207 °C. It was in excess of the

activation heat of hydrogenation, RT2 d In Vh/dT, by 4 ~ 5 kcal throughout. Twigg and Rideal [68]

remarked that the equilibration was much faster in the absence of ethylene than in its presence and,

with reference to the result of figure 16, that the

plots of 1 — u against *H at 156 °C and below ac- cumulated around one straight line (indicated by a broken line in fig. 16) which passed a point xH = 0.33 on the axis of abscissa; other straight lines were obtained at higher temperatures, and these

intersect the first line on the axis of abscissa.

Horiuti [8, 9] has accounted for these experimental

results by theoretical calculations on the basis

of the associative mechanism and predicted, as

18
FIGURE 16. Nonequilibrium fraction 1— u versus deuterium

fraction xH of hydrogen in course of catalyzed deuteration of

light ethylene over Ni-n4re [68],

u = ['HD]/['HD]eg . ['HD]: concentration of HD. [‘HD]eq : concentration of 'HD

which would result if existent hydrogen were brought to equilibrium with reopect to the reaction 'H L

» + Du

* = 2HD.

elucidated in 14.4, that the slope of curves such as those indicated by broken lines in figure 16 against xH -axis increase considerably when the temperature

is lowered below those in the experiments of Twigg

and Rideal [68], so that curves run down almost

vertically along a perpendicular atxH = 1 . Matsuzaki

[115] confirmed the results of Twigg and Rideal’s ex- periments by tracing them, on the one hand, and

observed relations between 1 — u and xH at temperatures as low as 0 or —25 °C as shown in figure 17,

Figure 17. Experimental results on the relation between 1 — u and xH in course of deuteration of light ethylene over nickel

Pe. o = p». o = 10 mm Hg.

on the other hand, in semiquantitative agreement

with the theoretical prediction of Horiuti [8, 9] as described in 14.4.

5.1.3. Farkas and Farkas [85] experimented with

platinized platinum foil on the parahydrogen con- version associated with the catalyzed hydrogenation.

Table 10 shows the half-life values tc and T/,, re- spectively, of parahydrogen conversion and cataTABLE 10. Parahydrogen conversion associated with hydrogenation of ethylene over platinized platinum foil [85]

Reaction

temp. °C

Initial partial pressures, mm Hg Half-life time, min.

T'e.o PH,0 Parahydrogen

conversion, rc Hydrogenation, Th

25 40 21 80 80

25 0 21 14 0 0 21 72 0 0 40 6

0 19 40 50 13 23 0 15 8 24 42.5 17.5 45 45

27 0 12.5 16 27 36.5 12.5 45 45

lyzed hydrogenation from 0 to 27 °C. We see from

the table that the presence of ethylene retards the

parahydrogen conversion as in the case of nickel and

that tc and Tn are the same in the presence of excess

ethylene, whereas rc is much greater in the presence

of excess hydrogen, or the relative rate of parahydrogen conversion is much smaller than that of

hydrogenation.

The optimum temperature was found at 160 °C

for 20 mm Hg ethylene and 40 mm Hg hydrogen,

and the activation heat of the catalyzed hydrogenation below the optimum 10—11 kcal [85],

which equaled the activation heat of parahydrogen

conversion in the absence of ethylene [85]. The

activation heat of the exchange was given as 22 kcal

by them.

Table 11. Exchange equilibrium between ethylene and hydrogen

in course of catalyzed deuteration over platinized platinum

foil [85] PEi 0 — 20 mm Hg, PHt 0 = 40 mm Hg

*H.obs : Deuterium atom fraction in residual hydrogen at the exhaustion of ethylene.

*H.caic : Deuterium atom fraction in equilibrium distribution between hydrogen and

ethylene.

Temp. °C

% Deuterium in residual hydrogen % exchange

l-*H,obs X10Q

1 obs 100*H. calc *^H, calc

25 99 37 1.5 54 95 40 8 79 80 41 34

100 75 40 42

120 63 41 63

146 59 42 70

187 51 43 86 235 48 44 93

273-052 0 - 68-4 19
5.1.4. Farkas and Farkas [85] observed the hydrogen exchange associated with deuteration of light

ethylene in the presence of platinized platinum

foil. Since, however, the deuteration was quite

rapid under the conditions where the hydrogen

exchange proceeded with measurable rate, the

deuterium content in residual hydrogen was measured on exhaustion of ethylene. Starting from a mixture of 20 mm Hg ethylene and 40 mm Hg

deuterium, they obtained the results shown in

table 11. The values xH , 0bs are atom percent of

deuterium in the residual hydrogen, xH> calc those

in exchange equilibrium calculated allowed for

the isotopic effect, and percent exchange is the

percent amount of exchange accomplished. Since

there occurs no hydrogen exchange between hydrogen and ethane under the experimental conditions [85], one can take from table 11 that the

exchange between ethylene and hydrogen is so rapid at around 230 °C that they practically attain

the exchange equilibrium.

5.2.

Modern Observations

5.2.1. Twigg [116] has catalytically hydrogenated

107 mm Hg light ethylene over nickel-kieselguhr

catalyst at — 78 °C either with 120 mm Hg equimolar

mixture of and D2 or with 120 mm Hg equilibrated mixture of ’H2 , *HD, and D2 to the exhaustion

of the light ethylene. He thus found that the infrared adsorption spectrum of the product, (A), of

hydrogenation of the light ethylene with equimolar

mixture of ! H2 and D2 was identical with that of the

product, (B), of hydrogenation with an equilibrated

mixture of ‘H-2, ! HD, and D2 , and that the identical

spectra of (A) and (B) were different from the infrared absorption spectrum of an equimolar mixture,

(C), of C2 'H6 and (VHiD;?. He found [116], moreover, that the conversion of 75.8 mm Hg parahydrogen over the same catalyst at the same temperature

was almost inhibited by coexistent 48.9 mm Hg

ethylene and that deuteroethylene was scarcely produced by catalyzed deuteration of light ethylene at — 37 °C over the same catalyst.

The result that (A) and (B) have the same infrared

absorption spectra but that of (C) is different ex- cludes the possibility of hydrogenation being

effected by a single act of addition of a hydrogen

molecule to ethylene but verifies the mechanism of

hydrogenation through dissociated hydrogen atoms.

5.2.2. Turkevich, Bonner, Schissler, and Irsa [117]

followed the catalyzed deuteration of light ethylene over nickel wire by mass-spectrometric analysis

of the product in several stages of the progress of

deuteration. The catalyst of nickel wire was mounted

in a reaction vessel, oxidized at 600 °C, reduced at 330 °C and, before every run, pretreated in deuterium gas at 300 °C. The reaction vessel was kept at 0 °C, deuterium was first, light ethylene subsequently admitted over the catalyst. The reaction was started by applying an appropriate current to the wire to keep it at 90 °C for a recorded time, and

the product thus obtained was analyzed. The results are shown in figure 18, where any curve, A„ or E„,

gives the partial pressure of ethane-d,, or ethylene-o?n against percent of ethylene deuterated. C2 'H6 was

the predominant initial product of deuteration, as seen in the figure, contrary to the expectation of

the authors [117] of finding CVH4D9 instead.

5.2.3. Kemball [76] followed the deuteration of light

ethylene at — 100 °C over films of Ni, Fe, Rh, and W,

respectively, evaporated on glass wall kept at liquid

nitrogen temperature, by analyzing the reacting

gas that leaked steadily through a capillary into a mass spectrometer. Table 12 shows the relative

0 20 40 60 80 100 DEUTERATED % ETHYLENE

DEUTERATED % ETHYLENE

Figure 18. Product of deuteration of 10 mm Hg light ethylene

with 20 mm Hg D2 over Ni wire at 90 °C [117]. PA „, Pe„: partial pressures of A„ =C2 'H,;- n D„ and E„ = C.'Hi-jiD,.

20
Table 12. Relative amounts of ethylenes-d„ = En and ethanesdn = An in the initial product of deuteration of 2.7 mm Hg

light ethylene with 8.1 mm Hg deuterium over evaporated metal

films [76].

Evaporated film Ni Fe Rh W

React, temp., °C -100 -100 - 100 - 100

E„ E, 46.7 55.5 34.4 7 e2 13.2 9.4 7.0 0 e3 2.7 1.3 1.7 0 e4 0.7 0.2 0.9 0

A„ Ao 7.8 13.7 8.4 3.1 A, 12.5 9.2 14.4 14.7 a2 9.5 6.6 15.8 69.8 A3 4.0 2.4 7.4 4.5 a4 2.0 1.0 5.0 0.7

A.-, 0.8 0.5 3.6 0.2

Afj .2 .2 1.4 0

amounts of different ethylenes-<4i and ethanes-c/n in the initial stage of the deuteration. In case of

tungsten, deuterium is hardly taken up at all by

ethylene and the result is marked by the maximum

abundance of C2

1 H4D2 among the ethanes-c/n . It was found [76] that the total number of moles

of ethane as well as the number of deuterium atoms

taken up by a definite amount of ethylene increases

proportional to the time of reaction. Table 13 [76]

shows initial values of rate of ethane formation, Vh,

and exchange rate of ethylene, vex> E . The kinetics

of both reactions was found to correspond to m = 0

and n = 0.5. The activation heats derived as usual

from both rates are approximately uniformly 5 — 6

kcal for W and 7 kcal for Ni, Fe, and Rh. Table 14

shows the relative amounts of ethanes-t/n on ex- haustion of ethylene by deuteration [76]. 5.2.4. Miyahara and Narumi [114] conducted a complete analysis of the product of catalyzed deuteration of light ethylene in the initial stage of deuteration over freshly evaporated nickel surface F (cf. 2.8.3) as shown in tables 15 and 16. “Deuterated

percent C2 H4 ” is the amounts of ethane in percent

of the initial amount of ethylene which were

identified with the decreases of total pressure

in percent of the initial partial pressure of ethylene. Tables 15(b) and 16(b) show the mass

spectra of run 2 in table 15(a) and run 12 in table

16(a), respectively, as observed at various stages

of deuteration. The first column of these tables

shows the mass spectra of gases sampled immediately after the introduction of the reactant

mixture into the reaction vessels, which were

assured free from ethane. The considerably high

values of M2 and M3 are interpreted as due to an

appreciable dehydrogenated adsorption of light

7 The previous result 2.9.1 over the F surface contrasts with the present one, which

is ascribed to a faster conversion of the F surface into an S surface in the present case, caused by the higher partial pressure of ethylene (10 mm Hg) than in 2.9.1 (0.05 mm

Hg partial pressure).

Table 13. Rates of deuteration and hydrogen exchange of eth- ylene, v h and vex , E, on evaporated metal films [76]

t/j»: Percent C2H4 deuterated per min per 10 mg film.

i;ex E : Number of deuterium atoms transferred per 100 C2H4 molecules per min per

10 mg film.

Metal React, temp.

°C

Vh t^ex, E

Fe -100 1.54 3.60 Ni -100 2.30 5.25 Rh -104 18.0 18.2 W -99 3.42 0.26

ethylene on the fresh surface, F, as described in

section 2 , which is enhanced at the higher temperature in the latter case.

It is concluded from tables 15 and 16 with ref- erence to the optimum temperature, 137 °C, as inferred from the result in figure 19 (cf. 6.2), (1)

that the predominant product of deuteration at 0 °C, amply below the optimum, is C2 'H6 ; as in the case of Turkevich et al. [117], but switches over to C2 *

4 D2 as the partial pressure of deuterium is in- creased, ( 2) that 1 H2 or 'HD is hardly evolved at

all in course of the catalyzed deuteration of 10 mm

Hg light ethylene with equimolar deuterium below

the optimum, as seen from table 15(b), or, in other

words, that protium atoms from light ethylene hardly

enter hydrogen gas , 7 (3) that at 200 °C, in contrast

with the latter result, the predominant initial product of deuteration is C^'hL^, while great quantities

of 'H2 and 'HD are evolved from the beginning of

catalyzed deuteration as seen from tables 16(a)

and 16(b), and (4) that an appreciable amount of

deuteroethylene is evolved both at 0 and 200 °C.

5.2.5. Data are compiled in table 17 from table 3

with special reference to the catalyzed deuteration over an S surface of nickel [26], where the dehydrogenated adsorption of ethylene is substantially in- hibited. Parenthesized figures show the percentages

of the respective compounds-<4, in a random distri- bution of isotopes as calculated on the basis of the

total deuterium atom fraction in ethylene or in

hydrogen. It is concluded from table 17, referring

to the fact that the observed value 0.992 of yH is just that of original deuterium gas, ( 1 ) that hardly

any protium appears in hydrogen gas in course of

the catalyzed deuteration at —45 or —23 °C, temTable 14. Relative amounts of ethane-dn = An produced on ex- haustion of light ethylene by deuteration over evaporated metal

films [76]

Metal

Initial partial pressures React. temp. °C

Ethanes-rfn , %

Re.O mm Hg

Rh.O mm Hg Ao A, A2 A3 A, A5 A«

Rh 2.7 8.1 -104 11.5 27.2 29.1 13.7 9.1 6.8 2.6 Fe 2.7 8.1 -100 20.1 28.4 22.1 12.7 8.6 5.2 2.9 W 2.7 8.1 -99 4.8 15.5 70.5 6.7 1.6 0.5 0.1 Ni 2.7 8.1 -100 17.9 26.8 23.2 14.0 9.6 5.9 2.6 Ni 2.7 24.3 -92 12.4 29.9 25.4 14.3 9.7 5.9 2.4 Ni 8.1 24.3 -81 17.1 30.5 20.7 13.8 9.4 6.2 2.3

21
peratures which are amply below the optimum at ca. 30 °C as gathered from the table, whereas

above the optimum, ! H2 and 'HD appear approximately in accordance with a random distribution

of isotopes, (2) that ethylenes-c?,i appear in accord- ance with the random distribution of isotopes ir- respective of temperature and (3) that the activation

heat of catalyzed deuteration varies only slightly

with the total pressure as indicated by its value

Table 15(a). Relative amounts of ethylenes- dn = En and

ethanes- dn = An in the deuteration product of 10 mm Hg

light ethylene at 0 °C over a freshly evaporated surface F of

nickel film [114]

No.

of run

Initial partial pressure

of D2 mm Hg

Deuterated %

c2 h4

Relative amounts of hydrocarbons-dn, %

E, e2 e3 E4 Ao A, A2 A3 A, A5 A^

2 10 33 13 1 0 0 45 23 18 0 0 0 0

3 10 45 12 1 0 0 35 28 19 4 1 0 0

4 43 12 27 3 0 0 40 24 3 2 0 0 0

5 107 29 29 5 2 0 23 19 13 4 2 1 0

7 138 36 14 1 0 0 27 10 36 7 2 1 1

Table 15(b). Mass spectrum of reacted hydrogen gas of run 2

in table 15(a)

Deuterated %

c2h4 0 15 20 27 33

Relative m2 4 5 5 7 5 heights M, 2 2 2 2 2 of peaks m4 94 93 93 91 93

Table 16(a). Relative amounts of ethylenes-dn = En and ethanes- dn = An in the deuteration product of 10 mm Hg light ethylene

with equimolar deuterium at 200 °C over a freshly evaporated

surface F of nickel film [114]

No. Deuter- Relative amounts of hydrocarbons-dn, %

of ated %

run c2 h4 E, e2 e3 e4 Ao Ai A2 A3 A4 a5 Ao

n 20 38 27 13 0 4 6 7 4 2 0 0

12 31 25 25 11 3 3 8 12 7 4 1 0

Table 16(b). Mass spectrum of reacted hydrogen of run 12 in table 16(a)

Deuterated % C2 H4 0 13 31

Relative m2 11 35 47

heights M3 5 31 27

of peaks m4 84 34 26

7.2 kcal at 0.1 mm Hg total pressure, derived from

its rate given in table 17, and 8.4 kcal at 20 mm Hg

total pressure, as indicated in figure 19.

5.2.6. Kazanskii and Voevodskii [119] analyzed

mass-spectrometrically the products of catalyzed

deuteration of ethylene at 90, 135, and 185 °C in

the presence of palladium plate. Deuteroethylenes were hardly found at all at 90 °C but at higher temperature they were present in large amounts, as shown in figures 20(a), 20(b), and 20(c). The amounts

of deuteroethylenes produced at 135 °C, if repreFlGURE 19. Initial rate, v h . u , of hydrogenation of light ethylene

with protium (O, A, ) or deuterium (#. A, ) over fresh (F), once used (S) or carbided (C) surface of evaporated nickel film [114]. eE .o = eH .(,= 10 mm Hg.

Vh, o is the initial value of vi,

,

i.e., deuterated percent of ethylene per min. Each

curve is specified by the surface state, F, S, or C. and the activation heat derived from

the curve at lower temperatures. The optimum points for the F, S, and C surfaces are indicated by vertical arrows.

sented by the respective molecular formulas, are

in the order of C2 'H3 D > C2 'H2 D2 > C2 1 HD;5>C2D4 throughout the reaction and attain their respective

maxima approximately at the same percentage of

deuteration of ethylene, whereas at 185 °C the

maximum shifts towards the greater percentage of

deuteration of ethylene the higher the number n of

(VH-i-nD,, as seen in figures 20(a) and 20(b). The

distribution of ethanes-G?,) over n does not vary with

temperature or the progress of deuteration and

reaches a peak at C2 'H4 D2 as seen in table 18. 5.2.7. Matsuzaki and Nakajima [120] showed by

adding the product of catalyzed deuteration of light

ethylene to a mixture of light ethylene and hydrogen, that the mass spectrum of deuteroethanes, i.e., the relative heights of peaks of mass numbers

greater than 30 remained unchanged, even if the

light ethylene and hydrogen are allowed to be catalytically combined in ethane, which verified that

22
Table 17. Relative amounts of ethylenes-dn = En and hydrogens-dn = Ha in the reaction product ofequimolar mixture ofC2 'H4 and D2 of

0.1 mm Hg initial total pressure over S surface ofnickel [26, 118] (compiledfrom table 3 [26])

React. temp.

°C

Deuterated

% C2 H4 Rate of hydrogenation

deuterated % C2 KU min-1

E„, % H„, % Deuterium atom

fraction in

E0 Ei e2 e3 e4 >h2 ’HD d2 c2 h4 h2

-45 2 3.5 93 7 0 0 0 0 1.6 98.4 0.017 0.992

(93 7 0 0 0) (0 1.6 98.4)

-23 10 18.2 90 10 0 0 0 0 1.6 98.4 0.025 0.992

(90 10 0 0 0) (0 1.6 98.4)

0 20 56.9 64 30 6 0 0 0 6 94 0.105 0.970

(64 29 5 2 0) (0 6 94)

28 43 98.0 66 28 5 1 0 2 10 88 0.103 0.930

(65 30 5 0 0) (0 13 87)

32 41 107.1 40 36 20 4 0 10 19 71 0.220 0.805

(37 42 18 3 0) (4 31 65)

75 38 97.0 29 38 24 7 2 30 29 41 0.263 0.555

(30 42 20 5 3) (20 49 31)

110 21 50.2 21 29 37 10 2 14 39 47 0.340 0.665

(19 30 38 10 2) (11 45 44)

Parenthesized figures show the relative amounts of En and Hn calculated assuming random distribution of deuterium. Those of En were calculated according to eq (12.32) with

*E(a> derived from observed values of XE ( a

)’s by eq (12.21.x). Those of H„ were similarly calculated.

23
Table 18. Relative amounts of ethanes-dn = An in the product

of catalyzed deuteration of 50 mm Hg C2 ’H4 with 200 mm Hg

D2 over Pd plate at 135 °C [119]

Deuterated °/o Relative amounts of ethanes-d„, %

c2 h4 Ao A, A2 A3 a4 a5 A6

10 0 25 50 12 8.5 3 1.5 25 0 25 50 12.5 8 3 1.5 37 0 20 49.5 13 10.5 5 2 50 0 24.5 46 14 10.5 3.5 1.5 70 0 26 41.5 13.5 12 5 2

ethane was not involved in the catalyzed hydrogenation.

5.2.8. Kowaka [121] has investigated the effect of

protium and deuterium diffused through palladium,

in advance of Apel’baum and Temkin [91], upon

C2 *H4 , or a mixture of C'2

1 H4 , and or a mixture

of C2

1 H4 and D>, respectively, contained inside a palladium thimble, by analyzing mass-spectrometrically the product. The palladium thimble was

evacuated, before use, at 800 °C for 2 hr, corroded

with aqua regia on both sides and again evacuated

at 800 °C with the aim of removing occluded hydrogen. Protium or deuterium were now let diffuse

toward the inside by electrolyzing protium or deuterium oxide, using the external surface of the

thimble as a cathode.

Table 19. Effect of deuterium diffused through palladium upon

C2 >H4 or C2 'H4 + >H2 [121]

Substance

upon which

deuterium is diffused

React. temp.

°C

React. time

min

Composition of product, mole %

ethyl- ene h2 >HD d2 eth- ane

100 mm Hg 40 30 52.5 6.7 0.9 16.2 23.7 (VH, 65 30 44.0 8.2 7.0 14.3 26.5 90 17 47.5 18.9 5.2 0 28.4 90 30 0 21.3 24.2 15.0 39.5

100 mm Hg 40 30 55.8 6.7 0.8 11.0 25.7 c^th + so 65 30 29.0 18.0 7.0 5.5 40.5 mm Hg 'H2 90 10 65.4 21.1 2.5 0 11.0

Table 19, figure 21(a) and figure 21(b) show the

effects of diffused deuterium upon 100 mm Hg

C2 'H4 and upon a mixture of 100 mm Hg C2 'H4 and 50 mm Hg *H2 inside the thimble, and figure

21(c) that of diffused protium upon a mixture of

100 mm Hg C2

] H4 and 50 mm Hg D2 . An appreciable amount of protium, to be traced back to light

ethylene, is evolved as

! H2 or

! HD, as seen in table

19, although the ^D-evolution is suppressed at lower temperature. As shown by figures 21(b) and

21(c), diffused hydrogen is considerably active,

and it is remarkable that in the former case the

maximum abundance switches over from CVHr to C2 'H4 D2 through the decrease ot temperature lust

by 25 °C.

DEUTERATED % C2 H 4

Figure 20. Ethylenes-dn = En in the product of catalyzed

deuteration of light ethylene [ 119].

24
n n n

Figure 21. Relative amounts of ethane-dn = An in the product of hydrogen atom diffused through

Pd upon €2*114 or €2^4 +H2 [121].

6. Isotopic Effect on Hydrogenation Rate

The isotopic effect on hydrogenation is defined as

ot = Vhi 1 ^) Ivhi^o)

where and iv,(D2 ) are the rates of hydrogenation of C2 W4 with pure protium and deuterium,

respectively, of the same partial pressure under

otherwise identical conditions.

6.1. Tucholski and Rideal [67] observed the rates,

and of catalyzed hydrogenation with

*H2 and D2 , respectively, in the presence of nickel

wire oxidized at 600 °C and reduced at 330 °C.

Activity lost by prolonged use was restored by keeping it at 200 °C in ca. 0.1 mm Hg protium or deuterium. The results are shown in table 20. The

optimum temperature is around 139 °C both in

the cases of t>/,(

1 H2 ) and f/i(D2 ), as seen from the

table, whereas the optimum of u/i(D2) was reproducibly located at 160 °C in another series [67]

of experiments by the same authors [67]. Table 20

Table 20. Isotropic effect a = v h('H2 )/vh (D2) on hydrogenation

rate of light ethylene on Ni wire [67]

D/,('H2 ), w,(D2): rate of hydrogenation with 'H2 or D2 . Pe.o = 3 mm Hg./>H , 0 = 5 mm Hg.

React, temp., °C 0 17 120 139 165 180 198

i>»('H2 ) mm Hg 0.40 0.58 3.1 3.36 1.90 1.01 0.81 min -1 i^(D2 ) mm Hg 0.24 0.38 2.25 2.54 1.84 1.34 0.54 min -1a 1.66 1.52 1.38 1.32 1.03 0.75 1.5

shows that a decreases gradually with rise of temperature down to unity or below around the optimum

and increases with temperature above it.

Figure 22. Initial hydrogenation rate, vh , of light ethylene

with equimolar protium or deuterium versus 10 3/T °K [118].

^e. o+ PHt o = 0.1 mm Hg.

Vh, o is the initial value of vi, given in hydrogenated percent C2 H.1 min -1

. ‘Ho. S, 4.8

kcal, etc., on the curves signify the hydrogenation with protium over S surface and the

activation heat determined at lower temperatures 4.8 kcal/mole, etc., respectively.

6.2. Miyahara and Narumi [114] and Miyahara [118]

observed the initial rates, o(‘H2 ) and f/i.o(D2 ), of

hydrogenation of light ethylene with equimolar

protium or deuterium over a surface of evaporated

nickel film at surface state, F, S, or C (cf. 2.8.3), at different temperatures and at different initial total

25
pressures. Figures 19 and 22 show the results obtained at 20 mm Hg [114] and 0.1 mm Hg [118]

initial total pressure, respectively. The values

of a derived in both cases of total pressure are shown in figure 23, with curves marked with S,

0.1 mm Hg, etc., which indicate the surface states of the evaporated nickel film and the initial total

pressures. The optimum temperatures of hydrogenation with ! H2 respectively appropriate to the sur- face states and the total pressures are shown by

vertical chain lines traced, respectively, up to the

Figure 23. Isotopic effect a versus temperature [118]. S and C signify the surface states of evacuated nickel film over which the initial value of hydrogenation rates with protium and deuterium, (

1

) and were

determined, and the associated figures the initial total pressure of the equimolar

reactant gas mixutre. The optimum temperature is shown by a vertical chain line traced up to the corresponding a-curve, which is relevant to the same surface state and

initial total pressure as is the optimum temperature, in accordance with the results of figures 19 and 22.

relevant a-curves. The values of a over the S sur- face decrease with temperature down to a minumum

at the optimum and then increase qualitatively in

accordance with the result 6.1. The a-values of

carbided film are much higher than those over S

surfaces as seen in figure 23.

Table 21. Activation heat and optimum temperature of cata- lyzed hydrogenation of light ethylene with equimolar protium

or deuterium over evaporated nickel films [26, 114, 118]

Surface state Initial total Activation Optimum

of evaporated pressure Hydrogen heat temp. °C

Ni film mm Hg kcal/mole

S 0.1 •HaDa

4.8

7.2 3050

C 20

'Ha 6.0 105 O

Da 8.4 137

r 0.1 ‘Ha 2.5 66

Li Da 2.5 110

c 20 'Ha 11.0 137

L. Da 11.0 165

Table 21 summarizes the results shown in figure

23. The optimum temperature of deuteration is 20 ~ 40 °C higher than that of hydrogenation with

protium over either surface.

Figure 24a. Catalyzed hydrogenation of ethylene over Cu(+MgO) in four isotopically different cases [103]. PE. o = Ph. o = 50 mm Hg. 40 °C. Figure 24b. Catalyzed hydrogenation of ethylene over Cu(+MgO) in cases of CVlh + 'FU (broken line) and CaD.) + ‘H> (full line) at different temperatures [103]. Pe .o = Ph.o = 50 mm Hg.

26
6.3. Table 22 shows the results obtained by Klar

[104] with an iron catalyst prepared by thermal

decomposition of iron oxalate followed by reduction

different temperatures, as shown in figure 24(b).

The ratio of the initial rate of C2

1 H4 + 1 H2 to that

of C2 'H4 + D2 was found unity at 20 °C with a fresh

Table 22. Ratio, a = v h('H2 )/v h(D2 ), between the hydrogenation rates of light ethylene with

protium vh ('H2), and that with deuterium vh(D2) over iron catalyst [104]

React.

temp., °C0 25 40 55 75 100 125 150 175

v„(’H2 ) 0.005 0.0127 0.0253 0.0517 0.110 0.207 0.271 0.217 0.18

a 2.5 1.69 1.58 1.67 1.22 0.98 0.79 0.56 0.51

of the resulting oxide. The observations were con- ducted with equimolar mixtures of ethylene and

hydrogen of ca. 2 mm Hg total pressure. It is re- markable that a is smaller than unity, indicating

that deuterium reacts faster than protium, above

100 °C. It is inferred from the table that the optimum temperatures of hydrogenation are 125 and

150 °C with protium and deuterium, respectively,

and the activation heats of hydrogenation with protium and deuterium are 7.5 and 9.5 kcal/mole,

respectively, below the optimum. No description

is given in the original paper [104] of the unit of rate.

6.4. Table 23 shows the isotopic effect on the hydrogenation rate of light ethylene over copper catalyst

[122]. The isotopic effect on the homogeneous hydrogenation rate is appended for reference. The catalyst

Cu(+ MgO) was the reduction product of a mixture

of oxides of Cu and Mg. In the presence of the latter

catalyst, Joris, Taylor, and Jungers [103] observed

the course of hydrogenation of ethylene in four

isotopically different cases at 40 °C, as shown in

figure 24(a), and also the course of hydrogenation

of C2

1 H4 + 1 H2 and of C2 D4 + 1 H2 comparatively at

catalyst but 0.75 over a catalyst whose activity had

declined with 20 repeated uses. The activation

Table 23. Ratio, a = vh (

I H2 )/v h (D2), between the hydrogenation

rates of light ethylene with protium, vh(’H2), and that with deuterium, vh(D2) over copper catalyst [122]

Catalyst

React, temp.

°r

... - 1 =

Initial partial pressure mm Hg a c2 >h4 h2

Cu [123] 0 375 375 2

Cu (+ MgO) [103] 2040

50

50 50

50

2

2.5 Homogeneous reaction

[123] 534 ~ 567 190 580 2.5

heats of the reactions of C2

1 H4 + *H2 and C21 H4 + D2 were found to be 11.5 and 12 kcal/mole, respectively, over a fresh catalyst.

7. Supported Catalysts

7.1. Nickel-kieselguhr catalyst is of frequent practical use for hydrogenation but its behavior is remarkably different from that of unsupported

nickel catalysts in the following points.

(1)

Ethylene or propylene does not polymerize

over unsupported reduced nickel powder at 100 °C

for several tens’ of hours but does perceptibly so over 15 percent nickel kieselguhr at 0 °C within

1 hr [124],

(2) The exchange of hydrogen atoms between

C2

1 H4 and C2 D4 at room temperature [24] is barely

perceptible over nickel wire of 730 cm2 area, and

even at 300 °C it takes more than 3 hr to attain an exchange equilibrium over nickel wire of 990 cm2 area [125], whereas the exchange is completed at room temperature within several minutes over

17 ~ 19 wt percent nickel-kieselguhr catalyst [125].

(3) No deuteroethylene was produced in course

273-052 0 - 68 -5 27
of catalyzed deuteration of light ethylene over 60

wt percent nickel-kieselguhr catalyst both at —50

and + 50 °C [126] as shown in table 24, in contrast

with the result 5.2.4 (4), which showed that an appreciable amount of deuteroethylene was evolved

over unsupported nickel. A mere 0.45 or 5.2 atom

percent protium were found [126] in hydrogen gas

at —50 or 50 °C, respectively, at the end of the

experiments. The absence of deuteroethylene in

the deuteration product of light ethylene was also

observed by Twigg [116] in the presence of nickelkieselguhr catalyst as mentioned in 5.2.1.

(4) Table 24 shows no preferential evolution of

C2

X H6 in the initial stage of deuteration as found

by Turkevich et al. [117] in the presence of unsupported catalyst but constant relative amounts of

ethanes-G?„ in the deuteration product, with a maximum at n — '2 (C2

1 H4 D2 ) irrespective of temperature

and extent of deuteration.

7.2. No such distinct differences are found between

supported and unsupported catalysts of metals of

the platinum group, which cause less dehydrogenated adsorption of ethylene as seen in section 2. Bond [88] investigated the kinetics and the distribution of compounds-dn in the deuteration product of C2

x H4 in the presence of platinized Pt, 5 weight

percent Pt-pumice, 1 weight percent Pt-alumina,

1 weight percent Pt-sihca and 1 weight percent Pt- sihca-alumina. One gram of each catalyst was dried

in air, evacuated at 200 °C in a reaction vessel of

45 cm3 capacity, pretreated in hydrogen at 200 °C

for 12 hr and evacuated. Admitting C2 *H4 first and

D2 subsequently over the catalyst, the deuteration

was followed by total pressure decrease and by

mass-spectrometric analysis of the product at dif- ferent temperatures and partial pressures of reactants. The results indicated, as shown in table 25,

that no significant difference exists between the

five different platinum catalysts, except that C2

1 H4 D2 is distinctly predominant only in the cases of 1 weight percent Pt-sihca-alumina and 1 weight percent Pt-sihca. Neither is there any distinct difference

between the distributions of ethanes-c?„ at 50 and

100 deuterated percents of ethylene under similar conditions of partial pressures as seen in table

24 of nickel-kieselguhr catalyst. Bond et al. [88, 89,

94], also dealt with rates of hydrogen exchange,

which is not reviewed here, however, as this was

quite unintelligible to the present writers.

Table 24. Relative amounts of ethylene-dn = En and ethanes-dn = An in the product of catalyzed reaction of 1:10 molar mixture of

light ethylene and deuterium over 60 percent Ni-kieselguhr [126] PE . o = 44.7 mm Hg (— 50°C), 64.8 mm Hg (50 °C) (partial pressures computed from reported experimental conditions).

React, temp.

°C

React, time

min

deuterated %

C2H4

Relative amounts of hydrocarbons-^,,, %

Eo E, —Ao A,

7 'A2 A3 a4 A5 Ar -50 5 22 78 0 4.7 6.6 6.5 3.3 0.9 0 0

15 59 41 0 12.5 14.0 16.5 8.7 4.7 2.6 0 35 87 13 0 15.6 22.2 24.0 13.6 7.0 3.5 1.3 80 99 1 0 15.8 24.0 28.4 16.8 9.3 3.9 1.8 185 100 0 0 17.8 25.6 27.4 16.1 7.8 3.6 1.5

50 5 39 61 0 1.8 5.8 11.9 7.3 6.1 3.8 2.3 15 83 17 0 5.0 14.7 24.2 15.8 11.7 7.6 4.0 60 94 6 0 7.2 16.5 26.4 17.0 10.0 9.1 7.9

28
TABLE

25.

Relative

amounts

of

ethanes-d„ = An

in

the

deuteration

product

of

light

ethylene

in

the

presence

of

platinum

catalysts

[88]

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29
Table 26. Relative amounts of ethanes- d n = An and ethylene-d n = En in

Metal Pt Ir

temp. °C 0 25 54 102 150 150 150 -16 -16 -16 9 86 124 152

PF , o mm Hg 99 51 99 99 99 96 52 100 99 50 100 100 100 100 Ph. o mm Hg 98 60 98 98 98 29 188 100 26 237 100 100 100 100

Deuterated % C2 H4 Less than 10 for all cases Less than 15 for all cases

Ao 10.0 19.2 19.3 9.5 4.9 8.2 5.7 4.4 0 0 3.5 4.6 1.7 0 A, 32.6 27.2 28.2 24.3 11.2 13.0 11.1 30.1 32.0 32.8 32.0 25.7 21.3 18.5 a2 37.8 23.2 25.6 26.8 23.9 14.6 28.2 36.9 37.5 40.0 39.6 30.0 28.9 27.0 A3 6.8 10.5 8.7 7.5 4.3 2.2 5.2 14.7 13.8 14.4 12.0 12.5 11.0 9.8 a4 3.3 6.4 4.9 4.2 2.9 0.5 2.4 7.2 9.1 8.2 7.5 9.4 9.3 8.1 Relative A5 1.9 3.0 2.3 1.5 1.7 0.3 1.3 2.2 3.3 2.7 1.7 4.8 5.8 3.9 amounts % Ae 0.8 0.5 0.4 0.5 0.2 0.1 0.9 0.4 0.4 0.4 0.2 1.2 1.4 0.8

Ei 6.0 7.4 9.2 19.6 36.5 44.0 32.8 2.9 3.1 1.1 2.9 8.1 14.5 19.6 e2 0.8 2.7 1.2 4.5 8.6 11.4 6.6 0.6 0.4 0.2 0.4 2.8 4.3 7.9 e3 0 0.8 0.2 1.3 3.9 4.7 3.4 0.4 0.4 0.1 0.2 0.7 1.4 3.4 e4 0 0 0 0.3 2.1 1.0 2.4 0.2 0 0.1 0 0.2 0.4 1.1

Bond et al. [89, 95], conducted similar experiments with 5 mole percent metal-alumina catalysts

of Pt, Ir, Os, and Ru comparatively; the results are shown in table 26. The distributions of ethanes-c?,(

and ethylenes-c^ are similar for the supported catalysts of Ir and Pt but those observed on the supported catalysts of Os and Ru differ from the former

and between each other.

8. Carbided Catalysts

The activity of metallic catalysts, especially

nickel, declines in general irreversibly, as mentioned

in 2, on account of adsorbed complex produced by

dehydrogenated adsorption of ethylene. Jenkins

and Rideal [13] prepared a carbided surface by

keeping an evaporated film in ethylene at 190 °C

for 30 min. They found that the rate of hydrogenation

over the carbided surface was quite reporducible,

although smaller than that over the freshly evaporated surface by a factor of several tens. Taking

advantage of this reporducibility they investigated

the rate law on the carbided surface and discussed

the mechanism of hydrogenation. This procedure

has been extended to supported Ni [82, 83], Pd foil [87] and Pt wire [87], but it is questionable whether

the carbided surface preserves any intrinsic property of the basic metal surface.

8.1. Miyahara [26, 118] observed the adsorption of

ethylene and hydrogen by the catalyst in the course

of the hydrogenation of light ethylene, the kinetics

of the hydrogenation, the hydrogen exchange between ethylene molecules and the distribution of

deuterium in the product of catalyzed deuteration over F (fresh), S (once used for a run of hydrogenation) and C (carbided) surfaces of evaporated nickel

him; the conclusion was that F and S behaved similarly to each other, except that the dehydrogenated

adsorption of ethylene was inhibited over S, while

C behaved quite differently from both F and S. The

activity of C is smaller than that of S by a factor of

several tens; apart from that, C differs from S in the

following points:

(a) Ethylene is adsorbed by S and C approximately to the same extent in course of the catalyzed

io 3 /t°k

FIGURE 25. Initial hydrogenation rate, v hi », of light ethylene

with equimolar protium over carbided surface versus W'/T

°K [118].

Vh.o is the initial value of vt, given in hydrogenated percent C2 Hj min '. Figures

attached to a curve indicate the initial total pressure and the activation heat deter- mined from the part of the curve over the range of lower temperature.

30
the deuteration product of light ethylene over 5 mole % metal-y alumina [89, 95]

Ru Os

54 54 54 54 32 64 80 24 24 24 24 17 36 47

100 100 27.5 100 75 75 75 50 50 50 50 50 50 50

54 165 50 50 76 76 76 27 50 152 203 50 50 50

5.5 5.5 10.9 11.2 7.3 7.3 7.3 16 16 16 16 15 15 15

2.6 0.7 2.1 2.6 2.2 2.9 4.1 3.1 0 0 0 1.0 3.2 0

9.9 11.3 10.0 11.0 10.4 9.7 10.7 14.2 14.3 11.3 10.6 9.8 15.1 12.3 29.0 35.7 29.5 29.3 41.6 26.8 25.9 46.8 52.0 55.4 62.8 59.0 41.3 44.4

2.5 3.1 2.4 2.5 2.1 2.6 3.5 6.1 8.1 7.7 6.0 6.4 6.2 7.0 0 0 0 0 0 0 0 2.5 3.5 3.3 1.8 3.0 3.2 3.0 0 0 0 0 0 0 0 0.6 0.7 1.0 0.9 0.7 1.0 0.6 0 0 0 0 0 0 0 0.6 0.7 0.9 0.9 0.7 0.8 0.6

52.1 45.1 52.3 51.7 42.8 54.0 49.8 24.8 18.2 18.9 15.9 18.9 27.5 30.7

3.9 4.1 3.7 2.9 0.9 4.0 6.2 1.6 2.4 1.6 1.1 0.4 1.7 1.5 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

hydrogenation, whereas hydrogen is appreciably

adsorbed only by S but not by C (cf. table 2) [26].

(b) The optimum temperature of hydrogenation

over C is ca. 30 °C higher than that over S (cf. figs.

13, 19, and 22 and table 21) [118].

(c) The activation heat over S at temperatures

below the optimum is 5 ~ 6 kcal/mole and practically independent of the total pressure of the

reactant gas mixture, whereas that on C below the

optimum increases from 2.5 to 11 kcal/mole with

increase of the total pressure from 0.1 to 20 mm Hg

[118] (cf. table 21 and figs. 19, 22, and 25).

(d) The distribution of deuterium in hydrogen in course of the catalyzed deuteration of light ethylene

is equilibrated over C, whereas it is not over S,

although the deuterium in ethylene is of random

distribution in both the cases [118] (cf. tables 17

and 27).

TABLE 27. Relative amounts ofethylenes-dn = En and hydrogens-dn = Hn formed by deuteration oflight ethylene by equimolar deuterium

on carbided nickel film at ca. 0.1 mm Hg initial total pressure [178]

React. temp.

°C Deuterated% C2H4

Rate of deuteration deuterated %

C2H4

• min -1

E„, % H„, %

Deuterium atom fraction in

E0 E, e2 e3 e4 'H2 'HD d2 c2 h4 h2

-23 1.2 0.86 88 12 1 0 0 2 4 94 0.032 0.970

(87.8 11.6 0.6 0 0) (0.1 5.8 94.1)

0 1.0 1.26 80 18 2 0 0 3 6 91 0.055 0.956

(79.7 18.6 1.6 0.1 0) (0.2 8.4 91.4)

70 6.4 3.16 16 32 32 15 4 53 40 7 0.368 0.272

(16.0 37.1 32.4 12.6 1.9) (53.0 39.6 7.4)

110 3.1 3.75 19 32 32 14 3 53 40 7 0.340 0.272

(19.0 39.1 30.2 10.4 1.3) (53.0 39.6 7.4)

160 3.1 2.12 21 32 31 13 3 50 42 8 0.323 0.293

(21.0 40.1 28.7 9.1 1.1) (50.0 41.4 8.6)

31
9. Reaction Mechanisms

Representative mechanisms are here reviewed

which have been selected from those put forward

up to now for the catalyzed hydrogenation in th'e presence of metals, especially nickel. It is the con- cept of the rate-determining step, that is indispensable in dealing with mechanisms. Confusions

arise often, however, by giving it an ambiguous

definition and unconvincing applications. Therefore, a definition of the rate-determining step is advanced and its application illustrated by mechanisms here.

9.1. Dissociative Mechanism

Farkas and Farkas put forward a mechanism on

the basis of experimental results of the catalyzed

hydrogenation as well as of the associated reactions,

i.e., parahydrogen conversion and 1 H2_D2 equilibration, over nickel [2] and platinum catalysts [85].

They [2, 85] assumed that the rate-determining step

of the catalyzed hydrogenation as well as of parahydrogen conversion 8 was the dissociative adsorption of hydrogen molecules, i.e..

Ho —» 2H(a), (9.1)

on the grounds that hydrogenation and parahydrogen conversion had activation heats of the same

magnitude, i.e., 10 — 11 kcal/mole, and a constant

ratio of rates throughout in spite of a widely varying

activity of platinum catalysts [85].

!) Ethylene was

assumed, on the other hand, to be adsorbed as C2 H4 —> CoH4 (a) (9.2)

and combine with 2H(a) so as to complete the

hydrogenation thus

C2 H4 (a) + 2H(a) > C2 H6 . (9.3)

The exchange reaction of ethylene was assumed

by them to occur separately, through a step of

dissociation of ethylene, i.e.,

C2 H4(a) » C2 H3 (a) + H(a), (9.4)

(hence the name “dissociative mechanism”), on

the grounds that the activation heat of exchange

was greater than that of catalyzed hydrogenation

both over nickel [2] and platinum [85] as reviewed

in 5.1.2 and 5.1.3, respectively.

They attributed [85] parahydrogen conversion

and x H2-D2 equilibration to step (9.1) and its reverse, on the one hand, and their inhibition to the

preoccupation of sites of these reactions by ethylene, on the other hand. However, the inhibition follows

necessarily from the proposed rate-determining

step (9.1) irrespective of the preoccupation, since

ethylene consumes the “moving spirits,” H(a)’s,

of the reverse of step (9.1) through step (9.3) at a

rate greater than that of the proposed rate-determining step (9.1).

9.2. Associative Mechanism

9.2.1. Horiuti and Polanyi [7] found that the rate of exchange between ethylene and water was

smaller than that between ethylene and hydrogen

by a factor of ca. 105 and that the exchange rate between ethylene and benzene under the same

conditions was still smaller [7] by orders of magnitude. On this experimental basis, they discussed

step (9.4) as proposed to be responsible for the

exchange. Let step (9.4) be in partial equilibrium;

C2 H4(a) is admitting H(a)’s through its reverse

including such ones originating from other molecules. The rate of the picking up is that of the reverse of step (9.4), which equals the rate of step

(9.4), i.e., a “unimolecular” dissociation; the rate of

the latter is constant irrespective of the activity of

H(a), apart from the effect of adsorption, hence the

rate of picking up H(a) is constant as well. Step (9.4) can hence not be responsible for the exchange,

8 Cf. 9.2.2 and 9.2.2.I. “Cf. 5.1.3.

insofar as the absorption does not make a difference

of orders of magnitude such as observed.

Horiuti and Polanyi [7], thus put forward with

reference to the experimental results [7], of the

wandering of the double bond, the scheme

C2 H4 h

H2

I b

d » C2 H4 (a)

H(a)

H(a) - -

II C2 H5 (ak

III

-> C2 H(i ,

(9.5)

where C2 H4(a) represents so-called associatively

adsorbed ethylene, in which the 7r-bond of ethylene

is broken and two carbon-metal bonds are formed,

and C2 H5 (a), termed half-hydrogenated state by

them [7], is an ethyl radical linked with the metal

by its methylene radical. The two hydrogen atoms

32
from a methylene radical of C2 H4 (a) and one from

H(a) assume equivalent positions in the methyl

radical of C2 H3 (a), so that the exchange results on

reversal of steps II. Step II in partial equilibrium is accelerated by

increase of the activity of H(a), hence its backward

act must be likewise accelerated. The rate of C2 H4 (a) embodying hydrogen atoms from H(a) depends in

consequence on the activity of H(a), in distinction

from the case where dissociation (9.4) is responsible

for exchange. The exchange rate of hydrogen atoms

between ethylene and water or benzene is hence by

far smaller' than that between ethylene and hydrogen, as observed, owing to their widely divergent

capacities of sustaining the activity of H(a).

9.2.2.

Scheme (9.5) is now discussed with special

reference to the rate-determining step of the rele- vant overall reaction. The rate-determining step is defined only for such an overall reaction where each

of the constituent steps has unique, definite stoichiometric number [127]. 10 The constituent step r of a stoichiometric number different from zero, is defined as rate-determining if the steady rate of the

overall reaction is given practically as that in the

equilibria of all constituent steps but r. These

partial equilibria determine the activity products, ax and aF , of the initial and the final system of r, irrespective of the kinetic particulars of any step.

The net rate of r is kx ax — kFaF or kx {ax — aF/K), where

K = kJkF is the equilibrium constant of r, which is thermodynamically definite irrespective of the

kinetic particulars of r. n The steady rate of the

overall reaction is thus proportional to ku which

alone involves the kinetic particulars of r, while

the other factor, ax — aF/K, of the net rate is thermodynamically defined by the system 12 of step r and

the conditions of the assembly in which the reaction

in question is going on. Step r thus literally determines the steady rate of the overall reaction through

its kinetic particulars which are exclusively in- corporated in kh

9.2.2. 1. A rate-determining step cannot be defined

in this way, e.g., for parahydrogen conversion in

gear with the overall reaction. Neither is it necessary

to assign a similar concept to this conversion, as seen later. We should admit a wording like “the

rate-determining step of parahydrogen conversion,”

if this occurs in gear with the hydrogenation, as designating a step assumed (by the broacher of the

wording) to have the same rate as the parahydrogen

conversion in question.

The rate-determining step of scheme (9.5) is now discussed on this basis. It is noted that step

III may be rate-determining, but it can never be in

10 The number of times a step occurs for every completion of the relevant overall reaction in the steady state. The set of steps, H + + e“ * H(a), 2H(a) * H2 and

H(a) + H+ + e~ » H2 has the stoichiometric numbers, (2, 1, 0) or (1, 0, 1) as given

in the order of the steps for the overall reaction, 2H + + 2e~ = H2 , where H+ is hydrogen

ion in solution and e~ metal electron. The stoichiometric number of each step of the above set is not unique. The stoichiometric number of every constituent step of scheme

(9.5) is unity uniquely for the overall reaction of eq (4.1).

11 All steps, heterogeneous or homogeneous, which have common I and F, have the same K quite independently from their rates, i.e., kinetic particulars, provided that all activities involved are referred to common standard states.

12 A set of particles involved in a step.

partial equilibrium since it practically lacks backward acts, as verified by result 5.2.7 that ethane is never involved in any constituent step of the cata- lyzed hydrogenation of ethylene. Nevertheless, any

step other than III, e.g., I b may be qualified as rate- determining, if kFaF is diminished by an amount

which is ignorable as compared with kx ax — kFaF , by reducing all steps but I b (inclusive of III) from

the actual steady state to equilibria.

9. 2. 2. 2. Let III be rate-determining, leaving the

other three steps in their respective partial equilibria. A step is kept in partial equilibrium notwithstanding the progress of the overall reaction, which

of course imposes a finite amount of net rate upon

the step, insofar as its forward and backward rates are large enough as compared with their difference,

i.e., the net rate. There hence occurs a lively ex- change of hydrogen atoms between gaseous ethylene

and hydrogen, as seen readily by tracing scheme

(9.5) with step III supposed to be arrested. Parahydrogen conversion and 1 H2 -D2 equilibration

proceed just as in the absence of ethylene, apart

from the effect, if any, of preoccupation of sites by

adsorption. Deuterium atoms are randomly distributed over C2 H4 , H2 and C2 H6 composed of the

former two throughout.

9. 2. 2. 3. If step II is to determine the rate, leaving

steps I a and I b in their partial equilibria, transfer

of hydrogen atoms between gaseous ethylene and

gaseous hydrogen is retarded in either direction.

Parahydrogen conversion and 1 H2-D2 equilibration

proceed as lively as in 9. 2. 2. 2. 9.2. 2. 4. In case of Ib determining the rate, leaving

I a and II in their partial equilibria, admission of

hydrogen atoms originating from gaseous ethylene

into gaseous hydrogen, is retarded whereas the reverse transfer occurs. Parahydrogen conversion

and 1 H2 -D2 equilibration are practically inhibited.

9.2. 2. 5. If I a determines the rate, leaving I b and II in their partial equilibria, parahydrogen conversion

and D2 equilibration will occur as in the

absence of ethylene and hydrogen atoms from

ethylene penetrate hydrogen while the reverse

transfer is retarded on the contrary to the case of

9. 2. 2. 4. Hydrogen atoms are randomly distributed over gaseous hydrogen and C2 H4(a), but not over gaseous ethylene and C2 H4(a) throughout; in the

particular case of hydrogenation of fight ethylene

with pure deuterium C2 H4 (a) is exclusively C2 D4 (a) so that gaseous ethylene should consist in the beginning of the hydrogenation only of C2 'H4 and C2 D4 but not of ethylene-d,, of intermediate composition.

9.2.3. Tables 3 and 17 show that deuterium in gas

keeps its atom fraction of 0.992 at —23 and —45 °C,

amply below the optimum at 28 °C, during the

catalyzed deuteration of fight ethylene. Protium of

ethylene got thus hardly into gaseous hydrogen,

whereas an appreciable amount of deuterium atoms

entered gaseous ethylene and became distributed

randomly there as seen by comparison of the observed percentage of ethylenes-d„ with calculated

value shown in parentheses. The tables show, on

33
the other hand, that above the optimum there occur

a rapid exchange between gaseous ethylene and

deuterium and a lively X H2-D2 equilibration, the

results below the optimum fit in exclusively with

the conclusions of 9. 2. 2. 4, while those above the

optimum fit in exclusively with those of 9. 2. 2. 2. We

are thus inevitably led to the conclusion that the

rate-determining step switches over from Ib below

the optimum to III above.

The same conclusion has previously been ar- rived at by Horiuti [9] from the analysis of experimental results of zur Strassen [64]. It may be noted

that the switchover in the rate-determining step is necessarily connected with the appearance of an optimum, thq excess of activation heat of exchange

over that of hydrogenation and other profiles of

the reaction, as shown by a statistical mechanical

theory developed in section 12. The term “associative mechanism” will be

used in what follows just to signify the kinetic

theory of scheme (9.5) without specializing in any

particular rate-determining step.

9.2.4. The chemisorbed states, H(a) etc., included in

scheme (9.5), are experimentally verified as fol- lows. Parahydrogen conversion and X H2 -D2 equilibration proceed over evaporated nickel films

perceptibility around — 100°C with a rate increasing

with temperature [128], 13 whereas the transition

from “normal” to “activated” adsorption with low

or high adsorption heat respectively occurs around — 150 °C as traced on an isobar [129] of hydrogen

adsorption over the same catalyst. These experimental results afford the basis for accepting the

existence of H(a) under the conditions in question.

Pliskin and Eischens [130] demonstrated infraredspectrometrically the existence of associatively

adsorbed ethylene, C2 H4(a), and the formation of

ethyl radical, C2 H5 (a), from C2 H4 (a) on admission of

hydrogen gas over adsorbed ethylene. Ethylene

and hydrogen are adsorbed simultaneously on S-film

without dehydrogenated adsorption of ethylene

as referred to in 2.E.1, which further confirms the

existence of three intermediates H(a), C2 H4(a), and C2 H5 (a) there.

9.2.5. The experiment of Apel’baum and Temkin

[91] on palladium indicates unambiguously a definite

fall of fugacity from gaseous hydrogen to adsorbed

hydrogen on the catalyst at 22 °C but none at 176

°C. Step Ib

is thus rate-determining at lower temperatures and in partial equilibrium at higher

temperatures, in accord with a similar conclusion

in 9.2.3 in the case of nickel.

9.3. Twigg and Rideal’s Mechanism

9.3.1. Twigg and Rideal [68] contradicted the dissociative adsorption (9.4) of ethylene as responsible

for the exhange reaction on the ground of Conn and

Twigg’s experiment [23] referred to in 2.7, which

showed that C2

X H4 and C2 D4 did not exchange

hydrogen atoms at 76 °C. Twigg and Rideal [68]

found, as reviewed in 5.1.2, that X H2 —

D

2 equilibration was inhibited by the presence of ethylene, and

that the plot of the nonequilibrium fractions 1— u of

hydrogen gas against its deuterium atom fraction, xH , converged into a single straight line for temperatures below and including 156 °C, as seen in figure

16. From these experimental results they gathered

[68] that X H2 -D2 equilibration was not effected by

step (9.1) but, as suggested by the latter close con- nection between equilibration and exchange, was

alternatively in gear with steps resulting in the

exchange between ethylene and hydrogen, as C2 H4 ^ C2 H4(a),

C2 H4(a) + H2 (a)

^

C2 H5(a) + H(a), (9.6)

and

They attributed the hydrogenation, on the other

hand, to a single step

C2 H4(a) + H2 (a) —» C2 H6 (9.8)

on the ground that the activation heat of exchange

exceeded appreciably that of hydrogenation [68, 69].

This mechanism of hydrogenation should lead,

however, to different products when light ethylene

is hydrogenated, in one case with an equimolar

mixture of X H2 and D2 , and in the other case with an

equilibrated mixture of X H2 , 'HD, and D2 . This is contrary to the observation of Twigg [116] in 5.2.1,

provided that the peculiarities of nickel-kieselguhr

used in the latter observation are ignored.

9.3.2. Twigg has thus revised the mechanism as

[116]

C2 H4 ^ C2 H4(a) C2 H4 (a) -f H2 (a)

^ C2 H5 (a) + H(a) C2 H(i 4 C2 H3 (a)^C2 H4(a) + H(a)

b

(9.9)

C2H5(a)^C2H4(a)+H(a), (9.7)

where H2 (a) is the physically adsorbed hydrogen

molecule.

13 Cf. Chapter 8 of ref. 18.

14 Cf. 9.2.1 and 9.2.2.2.

with the aim to account for the observed differ- ence between the activation heats of hydrogenation

and of exchange, by ascribing, respectively, different

rate-determining steps' 4 to them similarly to the

proposal of Twigg and Rideal [68] reviewed in 9.3.1. The rate-determining steps of hydrogenation and

34
exchange were thus indicated to be steps 7 and 4,

respectively, which have the same initial system,15 C2 H5 (a) + H(a), hence give rise to the same rate law for both the reactions, as observed.

Twigg [116] assumed next that below the optimum, step 7 was overwhelmingly faster than step 4.

If, then, the system C2 H5 (a) + H(a) is once created

by step 3, it should be converted with predominant

probability into C2 H6 rather than reconverted into

C2 H4(a) + H2 (a) through step 4. Step 3 thus determines the rate of hydrogenation,16 rather than

step 7, in conflict with Twigg’s statement. This is, however, just a contradiction in terms and, remaining true to the postulated predominance of step 7,

his arguments apply just by terminological revision.

The rate of rate-determining step 3 is k3 6C2H4 9U2 , denoting the rate constant of step n by kn and the

respective coverages by adsorbates C2 H4(a) etc. by

0C2 h4 etc. The latter rate is written, admitting the

proportionality of 9m to PH , as k3 dC2H4PH, which just

reproduces the rate expression of the catalyzed

hydrogenation given by Twigg himself. The steady

state condition of hydrogenation is now

kiOC2\i 4 PH — k4 9c2 h5 0h — k7 9C2Hb9H . (9.10)

Hence, we have below the optimum

k39c2H4^H = ^70C2 Hs^H > (9.1 1)

ignoring the rate of step 4 as compared with that

of 7 according to the postulate. The rate of ex- change is similarly &4 0C2H5 0H or, according to eq

(9.11), k3 (k4/k7 ) dcziuPn, which assures the rate law

of exchange to be the same as that of hydrogenation.

Above the optimum, it follows from postulate

k4 > k7 and eq (9.10) that the forward and backward

rates of step 3 are balanced with each other, hence

that step 7 functions as the rate-determining step,

provided that step 1 is also in partial equilibrium.

We are thus led to concluding from the kinetic

postulates of Twigg that the part of determining

the rate of hydrogenation is switched over from step

3 below the optimum to step 7 above.

As shown by Twigg [116], the activation heat of

exchange exceeds that of hydrogenation above and

below the optimum by E4 — E7 throughout, where

E4 = RT2 d In kjdT and E7 = RT2d In k7 /d T. The dif- ference E4 — E7 below the optimum is the difference

of the activation heat of the reverse of step 3 from

that of rate-determining step 3 as seen from

the above expression for the exchange rate,

k3 (k4 /k7 )dc2 iuPm the forward flow of the exchange

rate, k3 9C2H4Pu , is sparingly reversed, to a ratio

of k4 to k7 , to form the backward flow giving rise to the exchange. The ratio k4\k7 in the expression for

the backward flow is connected with the difference

between heights of the two energy humps

which enclose C2 H5(a)+H(a) as RT2d\n(k4/k7 )JdT =

E4 — E7 . Above the optimum, k4 \k7 equals directly

the ratio of exchange rate to hydrogenation rate,

the latter now being governed by step 7, hence the

difference is once again E4 — E7 . The above inference would illustrate that the dif- ference of activation heats provides no ground to exclude the reverse of step (9.1), assigned to be the

rate-determining step of hydrogenation, as done

by Farkas et al. [2], from being the “rate-determining step of exchange.” It may be noted, however,

that the switchover of the rate-determining step

that follows from the postulate of Twigg, can only

occur, according to the statistical mechanical theory

of the reaction developed in 11 and 12, between

steps having systems of different materials, 1

' such

as steps Ib and III of scheme (9.5), but it can scarcely occur otherwise, cf. steps 3 and 7 in scheme (9.9).

9.4. Jenkins and Rideal’s Mechanism

Jenkins and Rideal [13] revised the above mechanism supposing that the catalyst’s surface was

complex covered or carbided and capable of adsorbing further hydrogen but no more ethylene. 18

15 The initial and final systems of a step are its system, respectively, in the state before and after the occurrence of the step.

16 Equation (9.10) is expressed for k4 <S A-7 as

A^CjH./’h = WciHs^H "

(the 0’s are adsorbate coverages defined in the text); the first and the third member

are the rates of step 3 and 4, respectively, which are by no means balanced, hence

step 3 is by far not in partial equilibrium. We can bring the latter step up to equilibrium by increasing 0c,hA by a fact°r ki/kt. The rate of step 7 thus increases A7 /A4 fold. Since

the latter increased rate does not approximate by any means the steady rate, step 7

is excluded from being rate-determining according to 9.2.2. Step 3 is now similarly examined. By reducing step 7 to its partial equilibrium, vanishes when the rate of hydrogenation is k3dC2 n2 PH rather than A-3 0C2H,0h2 — A,0tsHs0H as in the steady state. Since A4 0C2Hl 0H is negligibly small by premise, the steady rate is closely approximated by that in equilibrium of step 7, i.e., k3 8C2H ,PH . Step 3 is thus duly rate-determining according to 9.2.2, provided that step 1 is also

practically in equilibrium. An actual example of the similar rate-determining step is given in 13.4.2.

17 Materials of systems of step I h and III of scheme (9.5) are H2 and C2 H, + H2 respectively, whereas those of steps 3 and 7 are commonly C2 H4 + H2 . 18 Just contrary to result 8. 1(a).

The exchange was postulated to occur under these

conditions through a step

C2 H4 + 2H(a)

^

C2 H5 (a) + H(a),

in which one of the two adjacent adatoms is picked

up, whereas both of them are captured to complete

the hydrogenation as C2 H4 + 2H(a) —» C2 H6 . (9.12)

They postulated further that the reverse of step

(9.1) occurs slower than step (9.12) at temperatures

below and faster above the optimum, respectively.

Below the optimum, 2H(a) once formed by step

(9.1) should be converted almost certainly into

C2 H6 by step (9.12) rather than reconverted into

H2 , so that step (9.1) is essentially rate-determining

for hydrogenation, while above the optimum step

(9.12) determines the rate, as shown by arguments

35
similar to those on steps 3 and 7 in 9.3.2. The rate- determining step of hydrogenation thus switches

over from step (9.1) below the optimum to step (9.12)

above, which is something in common with the

associative mechanism outlined in 9.2.1. Beeck [6] proposed, in advance of the above

revisal [13], that the hydrogenation proceeded

through step (9.12) and its rate-determining step

was the evacuation by hydrogenated desorption of

sites for adsorption of 2H(a) preoccupied by acet- ylenic complex, although this is inapplicable as remarked in 3.1.3.

9.5. Redistribution Mechanism

We have seen in 7.1.3 that hardly any deuterium

enters the ethylene in gas in course of its catalyzed

deuteration over Ni-kieselguhr catalyst, while

deuterium is abundantly contained and randomly

distributed in the ethane molecules thus evolved.

This result admitted, according to Wilson, Otvos,

Stevenson, and Wagner [126], of no explanation

by mechanisms proposed up to that time. They

put forward, for an explanation, the redistribution

mechanism in which a rapid exchange of hydrogen

atoms among “adsorbed hydrocarbon fragments,”

e.g., C2 H4 (a) or C2 H5(a), on the catalyst effected an exchange equilibrium or random distribution

of deuterium atoms among them as well as the

9.6. Adsorbed State

With special reference to the adsorbed state of

the intermediates implied, Semenov [131] proposed

the constituent steps of catalyzed hydrogenation

in terms of free valencies, V, furnished by metal

atoms of the catalyst. Ethylene is thus combined

with V to form a free radical as C2 H4 +E-^ Fen,—CH2 —. (9.13)

The free radical reacts upon H2 to form C2 H5 (a) or upon another V to form a stable C2 H4 (a) as VCU2 —CH2— +H2 -» HCH2—CH3 + H (9.14)

or HCH2—CH2—+ V-> FCH-2—CH2 V.

The H formed by step (9.14) is so unstable that it attacks C2 H5 (a) to form ethane as H+HCH2 CH3 -> C2 H6 +E.

hydrogenation through steps such as

2C2 H5 (a) —» C2 H4(a) + C2 H6 .

They [126] reproduced the fractions of ethanes-c?„

at —50 °C in table 24 approximately by its probability {6!/n!(6 — ti)!}jc”(1 —^A) 6- ” in random distribution, but the peak of distribution at n = 2

observed in 50 °C was not thus reproduced. They

similarly calculated the fraction of butane-d„ in the

deuteration product of light butylene, but the cal- culated abundance of butane-d2 fell appreciably

short of observation.

of Intermediates

In the case where sufficient C2 H4(a) and C2 H5 (a) are present, there occur frequently forward and

backward acts of the steps

H + FCH2 —CH2 E -> ECH2 CH3 + V

and

EH + HCH2—CH2 > ECH2,CH3 + V.

and the ECH2 — CH2 —’s react upon each other to form polymer, which poisons the catalyst. Semenov

[131] did not refer to step (9.1) of hydrogen chemisorption in this connection.

Bond et al. [132], has recently advanced the view

that the bonds which link ethylene to metal are not

a-bonds as admitted so in 3.1.2, but 7r-bonds between surface metal atoms and ethylene, with the

double bond of C2 H4 left intact, as in the case of

complex compounds between olefine and metal

salts, which is, however, not verified thus far and,

if it should be at all, makes no difference in the

kinetic treatments.

10. Current Theoretical Treatments

10.1. Outline

The rate v of combination, e.g., of species A and law in terms of the concentrations, [A] and [B], of

B distributed homogeneously in a macroscopic the respective species as phase is expressed according to the mass action

36
* cc [A][B], ( 10. 1 ) AHE — — RT2 d In bE/dT (10.6. E),

If either or both of species A and B are adsorbed,

as denoted by appendix (a), i.e., as A(a) or B(a), the

rate of combination is usually expressed by

v oc 0a[B] (10.2. A)

or

V cc Mb, (10.2. B)

where 6A and 6B are the fractions of the catalyst

surface covered by A and B, respectively.

Schwab [133] expressed the rate of the step

H2 (a) + C2 H4(a) —» C2 H6 , assumed by him to be rate-determining in the

catalyzed hydrogenation of rate vn according to eq

(10.2. B) as

Vh = khbE bftPEPy[ (1 + bEPE ) _1

, (10.3)

substituting 0C2H4 in eq (10.2.B) from Langmuir’s

adsorption isotherm:

^c2 h4 ~ ( 1 + 6EPE ) _1, (10.4)

and similarly for 6H2 :

$H2 = 6H^h(1 + Ph)~L

but ignoring buPH as compared with unity, where

kh is the so-called “true” rate constant. Schwab [133]

assumed that bEPE > 1 below the optimum and

bEPe 1 above the optimum, hence according to eq (10.4) that 0C2h4 1 or 0C2h4 ^ 0, respectively, or

in words that ethylene saturates the catalyst’s sur- face below the optimum but is desorbed as the

temperature is raised past the optimum, Tx . The

rate laws below and above the optimum are, in

consequence,

Vh — khbHPH (T < Tx )

and Vh = kh bEbHPEPH (T > Tx ), and the activation heats below the optimum,

Et<tx, and above the optimum, Et>tx

-> are Et<tx = E0 + A//h (10.5. a), and Et>t„ — Eo+ A//h + A//e = £V<7

, v + A//e , (10.5. b)

respectively, where

E0 = RT2d In kJdT (10.6.k)

is the so-called “true” activation heat ar 1

,s Cf. footnote 5 to 3.1.6.

and

-&HH = -RT2 d In bJdT (10.6. H)

are the adsorption heats of ethylene and hydrogen,

respectively. Schwab [133] determined, from the

plot of Vh/Pu against PE hy zur Strassen [64] as shown in figure 26, kt,bH and bE and hence Et<tx and AHE as

Figure 26. Proportional constant vh/PH of vh to PH versus PE [64].

vn'. hydrogenation rate in arbitrary unit.

Et<tx~ 7.3 kcal/mole, (10.7. E), — A//e = 17.3 kcal/mole. (10. 7. H)

He [133] thus described the optimum as the point

of desorption of ethylene. This theory of optimum

does not, however, fit in with new results as shown

in what follows. The quantity of ethylene adsorbed

on an S surface of evaporated nickel film in course

of the progress of hydrogenation (cf. table 2) was

found approximately constant and corresponded

to the coverage of 0C2H4 = O.33 over the temperature

range from —50 to 110 °C [61], which comprises the

optimum temperature, 35 °C; the above value of

0c 2 h4 was calculated from the observed quantity of

adsorption by geometric considerations on the

basis of 1015 surface metal atoms per unit BET

area, any two neighboring atoms among them being

taken as available for occupation by one adsorbed

ethylene molecule. This disproves the hypothesized desorption of ethylene, provided that the

observed amount of adsorption directly represents

those and only those molecules occupying the sites

of critical complex. 19 The above provision might be questioned with

regard to the active center theory, in the sense

that just a minute fraction of the observed amount

of ethylene adsorbed may block the active centers

and evaporate at the optimum to release them,

while the observation of the total adsorbed quantity

37
would be quite insensitive to this fraction. It is,

however, established [38] that the number of sites

of critical complex involved amounts to around

1015 cm-2

, as referred to in 3.1.6. Therefore, if ethylene is desorbed at the optimum to set these

sites free, according to Schwab’s hypothesis, then

the desorbed amount must be of about this magnitude, which is by no means negligible as compared

with the amount of adsorbed ethylene observed,

and would never escape detection; the approximately constant 0c2 h4 over the above temperature

range thus excludes the possibility of the desorption as responsible for the optimum.

The above hypothesis is further contradicted by

the observed dependence of the optimum temperature upon the partial pressure of ethylene.

Assigning the optimum to the point where

{d In viJdd/T)} pe , ph = 0, we have, on substitution

of Vh from eq (10.3),

RT2 d In hldT+{RT2 l(l + bEPE )}d In bE/dT

+ RT2d In bH/dT = 0.

The value of logi 0l bE at T= Tx

is obtained by in- tegrating eq (10.6. E) for constant AHE , as

logio&E = logio^E.o A//e /2.303/?Tx ,

1/TX — (1/3760) (9.3 — logio PE), (10.10)

(Tx in °K, PE in mm Hg) which deviates considerably from eq (4.3) as observed by Sato and Miyahara [80].

Jenkins and Rideal [13] expressed the rate of

catalyzed hydrogenation as Vh — k3 PE 6H2 according

to their mechanism (which was reviewed in 9.4),

where k3 is the rate constant of step (9.12). Denoting the rate constants of step (9.1) and of its re- versal with k\ and k3 , respectively, one can write

the steady condition of the reaction, as regards the

intermediates 2H(a), as

&iPh(1 — $h2 ) = ^2#h2 T hPe 0H2

or neglecting the rate of repulse of hydrogen adsorption, kx PH0n„ as compared with the sum of

the rate of adsorbed hydrogen leaving the adsorbed

state both by desorption (A'20H2) and by hydrogenation (k3PE 0H2), as

k\PH = A;2$h2 T k3 PE$H2

-

Eliminating 9H2 from this equation and the above

expression for the hydrogenation rate, Vh = k3PE dHi , we have

where logio bE , 0 is the integration constant. Eliminating RT2d InkhldT, RT2d ln6E /d7\ RT2d 1 nb^ldT

and bE from the above two equations and eqs

(10.6. k), (10.6.E), and (10.6.H), we have

1 Tx

(°K)

2.303R

-AHe

r -a//e -a//h -Eq

1 1oSio

6 e ,o(Eo+a//h)

logio PE

( 10. 8) The constant logio6E .o is evaluated from the above

linear relation as

logio&E.o — — 9.1. (10.9)

The value of (E0 + AtfH) is given by eqs (10.5.a) and

(10.7. E), while that ofA

HE is given by eq (10.7.H).

Substituting these values of (E0 +AHh ), AHE , and

that of logi 06E ,o from eq (10.9) into eq (10.8), we

have

Vh k\k3PEPH l (k-2~\~ k3PE )

,

(10.11)

which is of the same form as eq (10.3) due to Schwab

and agrees with the rate law observed by Jenkins

and Rideal [13] at the optimum temperature, 165 °C,

as given in table 7. They assumed, as reviewed in

9.4, that &2 ^ k3PE at temperatures below and

k3 > k3 PE above the optimum, hence v+ & PH or v+ cc PhPe, respectively, from eq (10.11), in accord- ance with experiments. The rate-determining step

is in consequence (9.1) at temperatures below but

(9.12) above the optimum, as discussed in 9.4. The

change of activation heat may occur, hence, by

switchover in the rate-determining step at the optimum because of the difference in materials of the

systems 20 of step (9.1) (EE) and that of step (9.12)

(H2 + C2H4) as mentioned in 9.8.2, whereas there

exists then little difference from the associative

mechanism, insofar as the hydrogenation is con- cerned.

10.2. Critical Review of Current Treatments

The formulation of rate of steps by the mass

action law referred to in 10.1. is applicable only in cases where the system (see footnote 20) of the step

is statistically independent, i.e., the system assumes

any state under given macroscopic constraints,

e.g., confinement to a definite volume, as if it were

20 Set of particles involved in the step.

21 A step is called homogeneous or heterogeneous according as its critical complex

[cf. footnote 5 to 3.1.6] is situated in a macroscopic phase or in a surface phase. A

macroscopic phase will be called simply phase in what follows.

alone under the same constraints. The statistical

independence is secured in cases where the species

of variable concentrations concerned are sparse

enough, whether the step be homogeneous or heterogeneous.21 The covered fraction of one-tenth

might be thought of as moderate, but the corre- sponding three-dimensional concentration is, for

1015 cm-2 sites and the appropriate thickness of

10-8 cm, 1015 X 10-1 X (10-8

) -1 cm~3 =1022 cm-3

, which matches the molecular concentration of

liquids. The applicability of the mass action law is

38
thus a problem which is rather more serious in case of heterogeneous steps than in case of homogeneous steps, just because of the different concentrations of species in the state of interest.

The applicability must of course be decided on

the basis of a general theory of reaction rates which

does not rest upon the statistical independence of

the system of the given step. Readers are referred,

in this regard, to an article “On the Theory of Heterogeneous Catalysis” by Horiuti and Nakamura

[134].

There exist two kinds of deviations from the

statistical independence of a system of a step in case of heterogeneous steps [134]. First, a species

is not admissible to a site of adsorption if the site

is preoccupied by another species. Secondly, there

exist in general repulsive or attractive interactions

between species which occupy their respective

sites exclusively. In the semiquantitative treat- ments presented in this monograph, we will be

content to take account of the former kind of deviation only, ignoring the latter throughout. Under this

limitation, the current treatments referred to in

10.1 are critically reviewed on the basis of the

general theory [134]; conclusions only are cited,

leaving out any detailed arguments.

(A) Equation (10.2. B) is exact, if -the critical

complex 22 of the step occupies the combined sites

of A and B.

(B) If the critical complex occupies a single site,

either of A or B, the exact equations is

oc0a[B| (10.12. A),

or v+ oc [AJ0b , (10.12.B)

respectively. Equations (10.12) are applicable when

A and B are alternative occupants of one kind of

sites, or when A and B occupy different kinds of

sites exclusively, or when either one of them is the exclusive occupant of any sites. The necessary

and sufficient condition for eqs (10.12. A) and

(10.12.B) to be valid is that the critical complex

occupies a single site, either of A or of B, respectively [134]; it is not necessary that either of A and

B is adsorbed and collided with by the other from

the gas phase. On the other hand, eqs (10.12. A)

and (10.12.B) do not apply even if the one from the

gas phase collides with the other one which is adsorbed, provided that the critical complex thus

formed occupies combined sites of A and B; in the

latter case eq (10. 2. B) holds instead.

It may be noted that eq (10. 12. A) is identical

with eq (10. 2. A).

11. Statistical Mechanical Formulation of Rates

Rates are statistical mechanically formulated ethylene statistical mechanically on the basis of

under the premise mentioned in 10.2 with the aim the associative mechanism,

of formulating the catalyzed hydrogenation of

11.1. Outline

The general theory assures, under the premise

in 10.2, that an exact result is obtained by the procedure of Glasstone, Laidler, and Eyring, which

treats sites of adsorption as if they were constituent species of a statistically independent sys- tem of the step. We start from eq (72) on p. 378

of “The theory of Rate Processes” by Glasstone,

Laidler, and Eyring, McGraw-Hill Book Company,

1941, for the rate v of a bimolecular step in case

of sparse coverage, i.e.,

V 2

sCgCg'Cs

kT ft h FgFgfs

by which two molecules of different kinds in gas,

of concentrations Cg and Cg

>, respectively, are combined on the catalyst; the catalyst provides sites

of adsorption for the molecules, each of them being

occupied by any of them at a given time, and the

22 Cf. footnote 5 to 3.1.6.

23 Under the present approximation, activated complex may be taken synonymous

with the critical complex referred to in 3.1.6.

activated complex 23 of the step occupies adjacent

two 'sites. Cs is the number of available single sites

per unit area, and 5 is the number of sites adjacent

to each site. Fg and Fg

> are the complete partition

functions of molecules of the respective kinds per

unit volume, which are substituted for the partition

functions in the original equation in Glasstone,

Laidler and Eyring’ s book, so that the Boltzmann

factor of the total elevation, €o, of the ground state

in the original equation is absorbed into the partition functions. The factor (l/2)sCs represents the

total number, Nt, of sites of the activated complex

per unit area under the above premise of a sparse

coverage. The quantities ft and fs are termed, by

the book’s authors, the partition functions of the

activated complex and of the reaction sites, re- spectively, whereas partition functions are defined

in this book only for a statistically independent

assembly and not for an adsorbed species or a site

which are not statistically independent. This

amounts to a leap of argument but can be rec- onciled by an alternative interpretation of ft and

fs as follows.

39
The factor fx in the above equation is read for

the partition function (complete) of the catalyst

with a single activated complex attached to a definite site, and fs for the partition function (complete)

of the bare catalyst. These definitions are acceptable since both subjects may be taken to be statistically independent. Since Fg and Fg

> are partition

functions of molecules A and B, both detached from

the catalyst, the product FgFg'fs is the partition

function of an assembly consisting of the bare

catalyst, A and B, all separated from each other.

The factor fs/FgFg'fs is hence the ratio of the probabilities of the state where the activated complex

is attached to a definite site and that where the

assembly is in the separated state; this ratio, when

multiplied by the universal frequency, kT/h, gives

the specific rate of the step in question, which pertains to a single pair of A and B on the definite site; the transmission coefficient is assumed unity

throughout the present treatment. Assuming the

physical identity of all sites of the activated complex on the catalyst, the last-mentioned specific rate times the number, Nx , of sites of the activated

complex gives the specific rate of the step which

occurs to this single pair of A and B per unit area. The overall rate of the step per unit area is now the

last mentioned specific rate times the number of

pairs of A and B, i.e., the product of the numbers

of both kinds of molecules. This product is reduced

to the product, CgCg

>, of the concentrations, with

regard to the above equation of v, by referring Fg and Fg

' respectively to unit volume. This equation

is readily generalized for any type of step under

the condition that its initial system is a set of gas

molecules and the catalyst surface is just sparsely

covered, as

v — (kT/h)N q

t ax , (ll.l.i;)

where ^ =f% Ifs , a\ = a ? ’ ai =

(ll.l.q), (11.1.1), (ll.l.i)

and Vi is the number of ith constituents of the initial system, I, in gas. The quantity q$ is by definition

the Boltzmann factor of the work required to add a system of the step in question to a definite site on

the catalyst as an activated complex, keeping the

whole assembly involved in statistical mechanical

equilibrium throughout the process [134, 135].

11.2. Function ax

Function ax in eq (ll.l.i;) is now developed for or with reference to eq (ll.l.i)

the sake of an expedient application. Equation (121)

in the same monograph of Glasstone et al., states a'laicfr . . . = a{a'"a^ . . . . that

Kc

fl }7 turn

1 L1

ivd N

1

P'11 f'b fc

A

1 B1 C

for the concentration equilibrium constant Kc of

the reaction in gas,

It follows, if a set of molecules in gas, 1 = ^ I'd,,

i

is in equilibrium with another set of molecules in gas,

T = 2 » th at V

aA. + 6B + cC + . . . — / L + mM + nN + . d\ — dy. (11.2.eq)

defined as where

r\ rmrn

j7 _ _iA m^1 n

• • • rarbrc U AL B UC

• • •

in terms of equilibrium concentrations, CL etc., of

molecules L etc., in gas. We have, equating the

above alternative expressions of Kc to each other

i r

(11.2.1), (11.2.1')

ay and av are called by Fowler and Guggenheim

[136] the absolute activities of species I, and Ir- respectively; the and ay are those of the sets

I and I'.

40
12. Statistical Mechanical Formulation of the Associative Mechanism

The statistical mechanical theory of rates in

section 11 is applied to the associative mechanism

in order to derive the steady rate of catalyzed

hydrogenation on the basis of associated reactions.

Functions k(s) appropriate respectively to steps 5 of

scheme (9. 5) are first derived; k(s) is the forward,

unidirectional rate of step s, under the supposition

that all other constituent steps are in equilibria.

12.1. Formulation of k(sYs

The formulation of k(s) is exemplified with step

II. The relevant activated complex is in equilibrium 24 with the initial system, C2 H4 (a) + H(a), which

determines the concentration of the activated complex, hence the rate. Suppose now the presence of

hypothetical molecules C2 H4 (g) and H(g) in gas

which are, respectively, in equilibrium with C2 H4 (a) and H(a). The activated complex is then in equilibrium with C2 H4 (g) + H(g). The forward rate of

step II, v+(II), is thus expressed according to eqs

( 11 . 1 ) as

14(H) — (kTjh)Nuii)QM1) aC2H4(g) aH(g)- (12.1)

aC2 H4 (B) aE and G'H(g) Ohi

where aE and aH are the absolute activities of

C2 H4 and H2 in gas, respectively. Substituting ac2 H4(g) and aH( g) from the above equations into

eq (12.1), 14(H) assumes its particular value,

Mil), i.e.,

Ar(II) = 0kT/h)Nm aE a\f. (12.2.II)

The k(s) s of other constituent steps of scheme

(9. 5) are formulated similarly as The rate A(II) is now by definition the particular

value of 14(H) in the case where all other constituent steps of scheme ( 9. 5) are in equilibria.

C2 H4 in gas is thus in equilibrium with C2 H4(a), hence with C2 H4(g) and H2 in gas with H(a), hence

with H(g). We have in consequence according to eq (11.2)

£(Ia ) = (kTjh)Nu1.)

a

E , (12.2.

a)

A"(I b ) = ( kTlh)Nt{lb) gMb ) aH (12.2.ib,

k(UI) = (kT/h)Nmi) q

m"aE aH. (12. 2. Ill)

12.2 Expressions for aE and aH

The functions aE and aH can be written according to eq (ll.l.i), developing F and FH statistical

mechanically and substituting \333Pi/kT (Pi in mm

Hg) for Ci, as

_j_ kT ( 27rmEkT) 3/2 2Tr2 (2TrlE kT) 3/2 Ue ~

1333Pe h? h

3

ft {

i “ exp (-^)}

' e^{-Rf)

and

II {l _exP (— hvjikT) }

1

j= 1

the vibrational partition function of ethylene, vj

the frequency of jth normal vibration and eE and eH the ground state molar energies of ethylene and

hydrogen, respectively. The vibrational partition

function of hydrogen is taken as unity. As to the

derivation of partition functions, readers are re- ferred to chapter IV of the book by Glasstone et al., mentioned in 11.1.

The functions aE and aH are now recast in the

kT (27rmHkT) 312 4-TT

2IHkT ( eH \

flH ~ 1333Ph ~h 2 eXP

V RTF form of

Pi

Qi, 0 exp where Qi, 0 and //, are

where mE and mH are the masses of ethylene and

hydrogen, IE is the geometric mean of the three

principal moments of inertia of ethylene, /H the

moment of inertia of hydrogen,

- 4 This postulate of the theory of absolute rate is often criticized (General Discussion

Reaction Kinetics,’' Trans. Faraday Soc. 34, 57, 71, 75 (1938)). Of course the equi- librium of such sort, could not always be established in the thermodynamic sense.

It has been shown [135], however, that, in case where the transmission coefficient is unity, the unidirectional rate may be exactly deduced according to the postulate even

in the absence of such thermodynamic equilibrium.

constant, by replacing T in the preexponentional

factors with TN exp (1 — TN/T) (a function which

for small differences between T and TN varies

closely to T) and assigning to TN a medium value

of the temperature range in question. T in the

vibrational partition function

12 FI {1 — exp (— hvjikT)}

j=i

41
can simply be replaced with TN , since it varies (12. 5. H)

little with temperature. TN is taken to be 373.15 °K

in the present treatment. We have thus

aE = Qei aH = F*hI C?H * (12.3.E), (12. 3. H)

where

Qe = Qe,o exp

/ eE + 4>RTN \

\ RT )'

(12.4.E),

= 1.057 X 1010 mm Hg.

It may be noted that the chemical potential p,, of species i is given as p,i — RT In a,, from_which

the partial molar enthalpy of species = — T(dinI dT) p , is derived particularly for ethylene

and hydrogen as He eE + 4/?7’N , Hh = 6n~\~— RT^,

(12.6.E), (12. 6. H)

Qu = Qh.o exp ( )

, ( 12.4.H)

_ kTN (27rmE kTN)3/2 2tt2 (2trWN)3/2 ^E ’° _

1333 h

3 h

3

12 n1=1 jl — exp e

4 = 3.939 X 1014 mm Hg.

(12. 5. E)

and the partial molar entropy, S* = — ( dp,i/dT) p, fol- lows as

Se = R In Qe,oIF*ei Sh = R In C?h.o/Ph-

(12.7.E), (12. 7. H)

The factor <jf'

5l(s = Ia , II, III) in eqs (12.2) is approximated as

q

tis) =exp (-e t<s) /RT), (12.8)

and

_ kTN (27rm HATN ) 3/2 in2IH kTN . ^H '° 1333 h

3 h2 e

where e*

(s) is the ground state energy of the activated complex of step s, ignoring the Boltzmann

factors of excited states, which may be fairly high on account of the narrow space of the site to which

the system of the step is confined.

12.3. Practical Expressions of k(s) s

Substituting a E , aH and Q

Us) from eqs (12.3)

and (12.8) into eqs (12.2) and further T in the

factor kT/h by TN exp (l — TJT), identifying all Nus’s with each other and referring to eqs (12.6),

we have

A;(I a) = o(Pe /Qe , o) exp {— A* H(la)/RT), (12.9.I a)

k(l h) = piPnlQn, o) exp (—A H{lh )IRT), (12.9.Ib)

k(U) = p(Pe/Qe , o)(PhIQh, o

)

1/2 exp (- A*H(11)IRT)

(12.9.II)

and

A'(III) = p(/>eIQe,o) (PhIQh,o) exp (-A*H(lll)IRT),

(12.9.III)

where

p = kTNNJh, (12.10.p)

Nt = NUs) , s = I a , I 5 , II, III, (12.10.7V)

A H(s) = //„„=<="+ firN

(12.11 (12.11 ,Ht

)

Hid a) r — He , Hki b ) r —

H

h ,

Hi(n)

r — He + — //H , Hi(iu) r = He + Hh ,

(12.12.

I

a), (12.12.I b), (12.12.11), (12. 12. Ill)

where I(5) r is the set of molecules of reactants

which constitutes 1(5) or is converted into 1(5) through steps other than 5, i.e.,

I(III)r =C,H4 + H2 , (12.13.III)

I(II) r = C2 H4 + 1/2H2 , (12.13.11)

I(Ia)r = C2H4, I(U- = H2 . (12.13.U (12.13.I b )

Equations (12.9) may be given in an alternative form

as

k(s) = exp ( — A" G{s)/RT), 5 = I a . I b , II, III

(12. 14. At) where

A

i G(s)=At H(s)-TAt S(s), (12.14.G)

42
A*S(s)=St -SI(s)r , = R In p.

(12.14.A* S)

(12.14.S*)

S

^i(ii)

r = Se “t- 1/2Sh , 5i(m)r = Sg + Sh*

I(I a )r ^E’ Sl( i b ) r — SH ,

(12.15.I a), (12.15.I b), (12.15.11), (12. 15. Ill)

The function p, as defined by eq (12.10.p), is the

partition function of activated complexes, with

energies referred to the appropriate ground states,

which transit the activated state unidirectionally once within unit time. 25 A* G(s) and A*S(s) thus

defined are the increments of Gibbs energy and of

entropy, respectively, of the whole assembly, caused

by bringing up the set I(s)r of reactants to the state where it is transiting the activated state unidirectionally once within unit time through steps other

than 5, all supposed to be in equilibrium.

12.4. Rate Equations in Terms of fe(s)’s

The forward and backward rates, v+ (5) and

v-{s), of the constituent steps of scheme (9.5) are

v+ (I a ) = (kTlh)NtqM^ aEn

v+ (I b ) = ( kT/h)Ntq *( W aH ,

v+ (II) = (kT/h)Ntq m) aC2 H4(a)a H(a),

v+ (III) = ( kT/h)Ntq mi) ac2H5(a)a H(a),

where aC2 H4(ah «H(a) and aC2 H5(a) are the absolute

activities of C2 H-i(a), H(a) and C2 H5 (a) defined as those of hypothetical gas molecules, (^tMg), H(g)

and C^hUg) respectively in equilibrium with (^FGla),

v+ (I a ) = A:(I a )

,

v+ (I b ) =A(Ib ),

t> + (II)=A(II)y(C2H4)y(H),

v+ (III) = A(III)y(C2 H5 )y(H),

where

given according to eqs (ll.l.r) and (11.1.1) as

v-(Ia ) = (kT/h)N%qW*>aC2H4( a),

v - (Ib ) = (kT/h)Ntq tab) a

2ma),

v- (II) = (kTlh)Ntq m)aC2 Hi(a)i

v-(lll) = (kTlh)Ntq^aC2H.,

H(a), and C2 H5 (a). Referring to eqs (12.2), the above

expressions of v+ ( 5 ) and y_(s) are written in the

form

t/-(Ia )=A(Ia )y(C2 H4 ), (12.16.IJ

v- (R) = ^(ib)y(H)2

, (12.16.IJ

t>- (II) = A:(II)y(C2H5 ) , (12.16.11)

v- (III) = A-(III)y(C2 H6 ), (12.16.III)

« H(a)/«H

1/2

, (12.17.E), (12.17.H)

a C2He!aE aHi (i 2 .i 7 .C2 H5 ), (12. 17. A)

y(C2 H4 ) — o C2H4(a)/aE. y(H) =

y(C2 H5 ) = a c2 H5<a)/ aE a H

1/2

i y(C2 Hj =

y(C2 H4 ) etc, may be called the activity coefficients

of the relevant species.

12.5. Steady State of Catalyzed Hydrogenation

The steady state is formulated by equating the

algebraic sum of rates of formation of each intermediate to zero. The stoichiometric number 26 of

each step of scheme (9.5) is thus found to be unity

- 5 Cf.II.A.2.c of ref. [ 1 34], The functions p. A^Cfs) and A^S(s) are defined there

with special reference to the critical complex (cf. footnote 5 to 3.1.6). This definition may be shifted to the activated complex without inconsistency.

2H Cf. footnote 11 to 9.2.2.

commonly with reference to reaction (4.1), without

any isotopic discrimination. Formulating the

steady state individually with respect to E„(a) = C2

1 H4 - n D„(a) (n = 0, 1, 2, 3, 4),1 H(a), D(a) and

A„(a) H C2

1 H5 -nD„(a) (n = 0, 1, . . ., 5), one can determine the relative amounts of E„(a) etc., and the

evolution rates of ethylenes-f/„, hydrogens-(7„ and

ethanes-rf,, as shown in what follows.

43
12.5.1. The rate Es of steady hydrogenation 27 in the

associative mechanism is given in terms of p+(s)’s

and p_(s)’s, on account of unit stoichiometric numbers for every constituent step, as Fs =v+ (s) — u-(s), 5 = I a , Ib , II, III (12.18)

or, substituting f+(s)’s and y_(s)’s from eqs (12.16). as

^s = ^(Ia){l-7(C2 H4 )} = ^(Ib ){l- 7 (H)2 } = A;(II){y(C2 H4 y(H)— y(C2 H5 )} = A-(III){y(C2 H5 )y(H) — y(C2 H6 )}. 12.19)

Eliminating y(C2 H4 ), y(H) and y(C2 Hs) from eq

(12.19), we have

partial pressures of reactants from vu and that from

Vs commonly as RT2d In VhldT = RT2 d In VJdT+RT.

The common difference RT is about within experimental errors of observation. We deal exclusively

with the steady hydrogenation for which Vs > 0.

It is inferred from eqs (12.19), that

(i) 0 <y(C2 H4 ), y(H), y(C2 H5 ), y(C2 H6 ) < 1,

(ii) 0<Es /(l-y(C2 H6 )) <A:(5), (5 = I a , Ib , II, III),

and also that,

(iii) as one of the functions A(s), say A(r), lies suffi- ciently below all other A(s'), every steps other than

r approaches equilibrium so that r tends to be rate- determining according to 9.2.2. Conversely, as step r tends to be rate-determining, all other rates,

Ar(s'), get greater than A(r).

y(C2 H6) —

Inference (i) is readily seen from eq (12.19), noting that Vs

. A(s)'s, y(C 2 H.i), y(H), y(C2 H.-,), and y(C2 H6 ) are all positive.

It follows from eq (12.19) and (i) that

Vs

A(II)

vs y

/ 2 vs k(lj A (III)

( 12 . 20)

Rates of the catalyzed hydrogenation of diverse

definitions have been introduced in reviewing the

treatments of various authors, symbolling them com- monly with Vh . These Vh s are related with Vs as

p/, = (A-771333E)Es ,

if Vh is given in the rate of partial pressure decrease

of either reactant in mm Hg in a closed space of

constant volume, V. We have

Vh = (AT/1333Pe E)Es ,

if Vh is the increasing rate of hydrogenated fraction

of ethylene of partial pressure, PE , in mm Hg or

vh = (kT/U33PH V)Vs

,

if vi, is the first order rate with respect to hydrogen,

which is referred to particularly as the rate constant, kh. These Vh differ from Es .by a factor which depends

on temperature and hence makes a difference

between the activation heat derived at constant

27 Vx here represents the number of ethane molecules evolved by the catalyzed hydrogenation per unit time.

2H The activity coefficient y(C2 H«) is expressed according to eqs (12.17. A) and (12.3) as

y(C2 H6 )— {PJPePh)((JeQhIQ^’>

where PA is the partial pressure of ethane and QA is a function defined for ethane

similar to QE as defined for ethylene by eq (12.4. E). We have y(C2 H6)= 1 in equilibrium according to eqs (11.2.eq) and (12. 17. A), hence, from the above equation,

^A.eqI?:K.eq^H.eq = QJQeVhwhere suffix equation signifies quantities in the equilibrium. The left-hand side is the equilibrium constant K,„ which is calculated from spectroscopic data [Landolt “Tabellen" Erg. III. c. (1936), p. 2609, 2622]. We have thus y(C2 HJ = Pa/Pk Ph A/ ,. which gives

the values shown in the text.

1 > l-l/s/^(I a )=y(C2 H4)>0, 1>1- Fs /A:(I b)<=y(H) 2 >0,

hence according to eq (12.20)

y(C2 H6 ) < 1 —VJk (I a ), y(C2 Hfi ) < 1 — VJk( I b )

y(C2 H«) < ( 1 - VJk(I b )) - ( 1 - VJk (I„) ) 1/2 VJk(ll) = ( 1 - vjk(h ) )

1/2 { (

1

- vjk( ib ) ) - vjk(U ) } < l - vjkdD

and y(C2 H»i) < 1 — Fs/Adlll), which are summarized in (ii). It follows from (i) and (ii) that < k(s). As k(r) of step s=r

gets smaller than k(s') of the other steps, s' # r, the coefficient of every k(s') in eq (12.19) tends to zero or, according to eqs

(12.16), every step s' approaches equilibrium. As to the converse

it is seen readily from eq (12.19) that the coefficient of k(r)

approaches 1— y(C2 HK ) while those of k(s') tend, respectively,

to zero. The k(s') should hence get greater than k(r), by the same equation, as r tends to be rate-determining.

It may be noted that y(C2 Hfi ) is extremely small

under the usual condition of experiments; y(C>Hfi)

is 3.6 X10- 27 at 200 °K and 2.7X10- 6 at 500" °K

for PE = PH = PA = 10 mm Hg. 28

12.5.2. The steady state is formulated with respect

to E„(a) = CVH-i-nD^a) in accordance with the

mechanism of exchange specified in 9.2.1., ignoring

isotopic differences in rates, as

Te„P + (I 3 ) — TEn (a)f-(I a )— TEn ( a)y + (II)

+

5 Tl y | 6 ri ^

^H(a)A En l

( a )

' (1 *H(a))TEn( a )

2 + n 6

*H(a>TE;) ( a )

^

(1 -* H(a)) ^E„+ i(a) MH) = 0.

n — 0, 1, 2, 3, 4,

(12.21. E)

where XEn is the mole fraction of E„ = C2

1 H4 . n D„

44
over C2 H4 in gas, AE „< a ) the mole fraction of E„(a) = C2

1 H4 -nD„(a) over C2 H4 (a) and xH( a) the atom

fraction of D(a) over H(a). The first two terms give

the net rate of creation of E„(a) by step I a and its reverse, and the third term the rate of consumption

of E„(a) by step II. The last term gives the rate of

regeneration of E„(a) by the reverse of step II, which is elucidated as follows.

The first term in curly brackets provides, when multiplied

by t; _ (II), the rate of formation of E„(a) from E„-ila) and D(a)

by step II and its reverse; two out of three hydrogen atoms on

the methyl radical of the half-hydrogenated state originate from

the methylene radical of E„-i(a), so that these two contain as an

average (n — 1 )

• 2/4 deuterium atoms; the third hydrogen atom

being deuterium, we have (n — l)/2+ 1 = (n+ l)/2 deuterium atoms in the methyl radical of the half-hydrogenated state, as

73 + 1 an average. The number of protium atoms is thus 3 —

= (5 — n)/2, one of which has to be given off by the reverse of

step II, which occurs with the probability of ——— X-=

7—

,

hence the first term. The second term in curly brackets repre- sents the regeneration of E,,(a) from A„(a), which acquired one

protium atom by step II. The methyl radical of the A„(a) has n/2

deuterium atoms and 3 — n\'2 protium atoms as an average; one

of the latter has to be given off for the regeneration of E„(a), which occurs with the probability of (3 — n/'2)/3 = (6 — n)/6, hence

the second term. The third term represents the regeneration of E„(a) which acquired one deuterium atom on reaching the half- hydrogenated state; its methyl radical has thus n/ 2 + 1 deuterium

atoms, and one of them has to be given off in order to regenerate

E„( a), which occurs with the probability of (n + 2)/6, hence the

third term. The fourth term is referred to the half-hydrogenated

state formed by combination of E„ + i(a) with 1 H(a). The methyl

radical, hence, keeps (n + l)/2 deuterium atoms exclusively

originating from the methylene radical of E„+i(a). One of (n + l)/2 deuterium atoms on the methyl radical has to be released by the reverse of step II, which occurs with the probability of (n + l)/6, hence the fourth term in curly brackets.

-Ar An(a)V-(II)-^A„(a)^+(ni) = 0,

(12.21. A)

where AAn ( a> is the mole fraction of A„(a) over C2 H.-,(a). The first term gives the rate of A„(a)

formation by combination both of E„_i(a) with D(a)

and of E„(a) with 'H(a), as represented by the two

terms in curly brackets, while the second and third

terms give the rates of consumption by the reverse

of step II and step III, respectively. Terms comprising P-(HI) have been ignored similarly, according to 13.4. 12.5.5. The fraction *E( a ) in eqs (12.21.H) and

(12.21.D) is related with AEn ( a)’s as

4*E( a ) = S

n^E«

(a> ( 12 . 21 .x)

n = 1

by definition. AEf! < a ) andA A?)(a) satisfy, by definition,

the equations,

2'YE„(a)=l, X^A n(a)==1 - « = 0 n = 0

(12.21.Ae ), (12.21.Aa)

Equations ( 12. 21) provide 16 equations for 13

unknowns, i.e., AEn(a)(n = 0, • • •, 4), xH( a >, *E(a) and AAn ( a)(n = 0,

. . ., 5). The 16 equations are not

all independent. Summation of eqs (12.21.E) over

n yields, with reference to eq ( 12.21 Jl e ), Mla)-Mla)-tMH) + MlI) = 0, (12.22.E)

12.5.3. The steady state is formulated with respect

to 'H(a) and D(a) similarly as

2(1—XH)y+(I b) —2(1—*H(a))t>-(Ib) —(1 —*H< a >)t> + (H)

+ v _ (II) _ (1 _ xH(a))p + (IH) = 0

(12.21. 1 H)

and

2xhv +(Ib) - 2xH( a )t’ _(Ib) - xH(a)v +(II)

+

2*E(a)+- *H(a) „ _(U) -XMa)V 4HI) = 0,

(12.21. D)

where *E( a ) is the atom fraction of deuterium in

C2 H4 (a), and the coefficient of f-(II) in eqs (12.21.H)

and (12.21.D) is the probability of 'H(a) or D(a) being

yielded, respectively, by the reverse of step II. Terms comprising y_(III) have been ignored according to conclusions 13.4.

12.5.4. The steady state is formulated with respect

to A„(a) = C2

l H5 _ n D„(a) as

summation of eqs (12.21. 1 !!) and (12.21 .D) gives

2t>+(I b ) — 2y_(Ib) — iMH) + f-(H) — iMHI) = 0,

(12.22.H)

and summation of eqs (12. 21. A) over n with refer- ence to eq (12.21 Jl a ) gives

r+(II) - Mil) - Mill) = 0. (12.22. A)

Equations (12.22) follow, however, directly from

eq (12.18) when similarly neglecting f-(III). It is thus premised that the v+(s) ’s and v_(s)’s comprised

in the above sixteen equations satisfy eqs (12.22).

Three out of the above 16 equations are in conse- quence dependent. Thirteen unknowns are determined as a solution of 13 independent equations.

12.5.6. The fractions, xE ( a > and xH( a ), are determined now asffiunctions of v+(sYs and p_(s)’ s. We

have, eliminating f_(I b) from eqs (12.22.H) and

(12.21. D)

3(xh - *H( a >)MIb) + (*e(b) _ -*H< a ))v-(II> = 0 , (12.23. a)

and summing up eqs (12.21.E) multiplied by n from

{*H(a) ^E„_!( a n= 1 to 4, referring to eq (12.21.x), )T (1 XH( a )) AE;i ( a )}f+(II)

45
4aE y+(I a ) - 4acE(a)i;_(I a) — 4zE(a)i; + (II) *E(a)

6xEi; + (Ia) + ^H(a)^-(H)

6v+(I a ) + i;-(II)

(12.24.E)

+

2 10

3

*H(a) + y *E(a)) V-(II) = 0, (12.23.B) and

where xE = ^ nxEJ^ is the atom fraction of deun = 1 terium in C2 H4 in gas. We have, eliminating i;_(I a) + f+(II) from eqs (12.23.b) and (12.22. E),

6(*e - *E(a))»+(Ia) + (*H<a> _ *E(a))V-(II) = 0. (12.23.C)

Equations (12. 23. a) and (12.23.c) are solved simultaneously for xE( a ) and *H(a) as

_ 2xE v + (l a)v-(ll) + *H fMlb)(6i;-t -(Ia) + MH)) *H<a> 2y + (I a)f-(II) + v+(Ib)(6i; + (I a ) + v-(ll))

(12.24.H)

The mole fraction of A„(a) over C 2 H5 (a), AA/( ( a), is obtained by eliminating (w_(II) + y+(III))/t; + (II) from

eqs ( 12 . 21 . A) and ( 12 . 22. A) as

^A n(a) = *H(a)AEn _ 1

( a) + (1 ~ ^H(a))^En (a)- (12. 24. A)

12.6. Rates of Reaction Associated With the Catalyzed Hydrogenation

The rates of the associated reactions are derived

as follows, ignoring the isotopic differences in rates.

12.6.1. Exchange rate in course of hydrogenation

is defined respectively for ethylene and hydrogen

as follows.

12.6.1.1. Let nE be the total number of hydrogen

atoms comprised in gaseous ethylene and xE their

fraction of deuterium. The rate of increase of deuterium atoms in gaseous ethylene, d(nExE)/dt is given in terms of the rate of penetration into gaseous

ethylene of hydrogen atoms originating from gaseous

hydrogen, LeX;E , and the rate of hydrogen atoms

given out from gaseous ethylene to gaseous hydrogen and ethane, L+ E , as

d(nE xE )/ dt = xh Lex> E xE V+ E

The first term on the right-hand side is the rate of

deuterium atoms transferred from gaseous hydrogen

to gaseous ethylene and the second term those

transferred counter from gaseous ethylene to gaseous hydrogen and ethane. V+ E should exceed

Vex> E by the rate with which constituent hydrogen

atoms of gaseous ethylene are lost by hydrogenation, — nE , i.e.,

L+ e = LeX)E —

n

E

.

28 Twigg and Ridea) [68| defined the initial exchange rate of hydrogen, vex , H , as vex , H = — *h at x E = 0 and xH = 1 as mentioned in 5.1.2., which is related with Pex , H according

to eq (12.25. H) as

fex. h = ( 1/oh) yex. H- The factor, l/n H . is given as kT{2 x 1333 P»V) in terms of the partial pressure of hydrogen, PH , in mm Hg and the volume, V, in which the gas mixture in question is confined. This factor makes difference between the activation heats derived at constant PH and

t'ex. h as

RT-H In vn. H/aT= RT*d In fex . »/dT+ RT

We have from the above two equations

^ex, E ^E^eI (xE Xy[

)

. (12.25.E) ^ex, e thus defined is called the exchange rate of

ethylene.

Similarly, the exchange rate of hydrogen is defined as 29

^e\, h~ nHXnl (xE —

x

H )

,

(12.25.H)

where nH is the number of hydrogen atoms comprised in gaseous hydrogen.

It may be noted that Eex , E and Eex H are not

necessarily equal to each other under the progress

of hydrogenation. For instance, if I b governs the

rate, a good amount of hydrogen atoms from gaseous

hydrogen is transferred to gaseous ethylene but

hardly conversely, so that VeXt E is significant but

Eex> H not- In the special case where nE , nH and the

total amount of deuterium, i.e., nExE + nHxH are kept respectively constant, we have nExE + n„xH = 0,

hence VeXyE — Eex , H according to eqs (12.25).

12.6.1.2.

Equations (12.25) are transformed with

reference to the associative mechanism as follows.

The rate of increase of deuterium atoms in ethylene

in gas, d(nExE ) Idt, is expressed as

d ( nExE ) Idt = 4n _ (I a)x E< a) — 4y + (I JxE

.

We have, on the other hand,

hE = 4f-(Ia) — 4y + (Ia)

hence from the above two equations

^E^E similar to the case of Vh and V, referred to in footnote 27 to 12.5.1. = 4(xE( a ) X^y-fla). (12.25 jc e )

46
Substituting nExE from the above equation into

(12.25.E), Fex , E

is given as

>/

e,. E = 4 ^

, L~/

E%-(Ia ). (12.26.E)

Equation (12.25.H) is similarly transformed as

= (12.26.H)

12.6.2.

Parahydrogen conversion is effected ac- cording to scheme (9.5), in course of catalyzed

hydrogenation, by step I b and its reverse. Let Xp

be the mole fraction of parahydrogen over hydrogen

in gas, i.e..

Xp Nh/Nh ,

where 1\

is the number of parahydrogen molecules

and NH the total number of hydrogen molecules.

We have by differentiation

Xp = K/NH -XpNJNH .

TVh and NH are expressed in terms of p + (I b) and

f -(Ib) as NH — Xp , oof — (Ib ) XpV + (I b ), /VH — f-(Ib) v + (Ib ),

where Xp> «, is the particular value of Xp reached in

equilibrium of parahydrogen conversion.30 Eliminating and NH from the above three equations,

we have

FP = =f-(Ib), (12.27) ^ p, oo A p which states that the rate of parahydrogen conversion, Lp , as defined by the second member of

eq (12.27) equals y_(Ib).

12.6.3.

The rate of 'H2 -D2 equilibration, Fq

. is defined as

Vq — NHu, (12.28.q)

where

W = A^ihd/^HD, eq (12.28.U)

and /Vi HDjeq is the number of 'HD molecules, which

would exist if hydrogen concerned were equilibrated. Fq is developed as follows.

1,0 Hydrogen evolved by the reverse of step I h must be of equilibriuni composition,

insofar as para- and orthohydrogen enter step I b with equal chance since, otherwise,

the catalyst should shift the equilibrium.

For a supposed equilibration of the hydrogen present ^i Ho eq + (V, HD. eq + Np.,D'j. eq

and

xH = (2yVD2 , eq + /V, HD eq )/2/VH ,

where suffix eq signifies particular values in the equilibration.

Besides,

^‘HD, eq ^*H2 , eq ^P'l. eq — 4

in the absence of isotopic difference of rates.

On elimination of /V, Hj> eq and /VDj , eq from the above three equations, we have

/V-HD,eq = 2jtH(l-^H)A/H- (12.28./V)

The ratio u is expressed by substituting/Vi H d. eq from the above

equation into eq (12.28.u) as

u = Nim/2x H (l ~xh )Nh

hence, by logarithmic differentiation.

(12.29)

“/“ ^‘hd/^.hd /Vh//Vh+

( l-^H xJ

Xh '

/VH in the above equation is expressed as

yVH = w-(Ib)-*’+(Ib)

and yVi HD as

yv ^iHD = 2^H(a)d ~ ^H(a))v-db) = H°

U + (I b ). /V H Hydrogen evolved by the reverse of step I b must be perfectly

equilibrated in the absence of isotopic difference of rates. The

rate of ‘HD formation by the reverse of I b is thus its rate, u_(I b), times the fraction. 2xH< a

)(l — xH< a )), hence the first term of the above equation. The second term gives the rate of consumption

of 'HD-molecules by step I b. i.e., its rate. c + (I b ). times the fraction of the number of ‘HD over NH. Eliminating N, m, NiHD and NH from the above four equations, we have, referring to eq (12.28.q).

r/ i\t ‘ f-*H(a)(l ^-H(a)) ] /T \ V*- N« u:

_

t -“r-

(l » )

,12 - 30)

12.6.4.

The rates of evolution, FE , Vi H , VmD, Vd.2

. and VAn . of ethylene-t/,, = E„, 'H2 . 'HD, D2 and ethane-c/„ = A„. are given in terms of AEn ( a), XAn (a), *H(a), v+(sY s and v-(sY s, as

VE=XEn ( a) v-aa ), n = 0, 1, 2, 3, 4, (12.31.E)

H 2 (1 -*'H(a))' (Ib)»I i hd 2xH( a

)(l *-H(a))t’-(IbL

^2 = ^

2H(a)i;-(I b ) (12.31. H)

and

47
^A n — {ATH(a)^A„ _,( a ) + (1 -*: H( a ))A A n( a ) }l7 + (IH),

71 = 0, 1, . . • ,6. (12. 31. A)

12.6.5. Let us assume that deuterium atoms are randomly distributed over En and E„(a), which is realized, where the associative mechanism is con- cerned, when y+(I a ) and f-(I a ) are large enough to give every ethylene molecule, be it in the gas or in

the surface phase (adsorbed), an equal chance of

acquiring deuterium. We have then

Ae „ = AE„( a> = (12.32)

Substituting X\„(a) and AAn l (a) from eq (12. 24. A)

into eq (12. 31. A), we have

VA n {a

yn-d )^En

_2(.a) H( a )( 1 ^H(a ))XE n _ pa)

+ (1 — X H(a))

2 ^E „( a )}y + (III)

n = 0, . . .,6, (12. 33. a)

x E or substituting AEn(a) etc. from eq (12.32) into eq

(12. 33. a), ^A n — _ 2^ -^Hfat^Efaf ( 1 — •*: E(a)) K_ "

+ 2

(„ - lj *H(a>( 1 - *H(atix&Cat ( 1 ~ *E(a) ) 3 “ "

+ (^)

(1 -^H(a))2 ^(a) (l

-*E(a)) 4 ~"} y + (III),

n= 0, ..., 6, (12.33.b)

Where combination vanishes, of course, for v > 4. In the special case where -^ H( a ) = ^ E( a) = , eq (12.33.b) is reduced identically to the equation

FA„=(6

re)r;d— rd6 -"!;^111), (12.33.c)

which indicates the random distribution of deuterium over ethane evolved.

13. Estimate of fe(s)’s

Rates of steady hydrogenation and various asso- ciated reactions were given in section 12. in terms of

v+(sYs and t>_(s)’s, which in their turn are determined by k(sYs according to eqs (12.16) and (12.19).

The rates, A(s)’s, are evaluated in this section by

adapting the theoretical relations to experimental

results. It may be noted that the steady rate, Vs , of the catalyzed hydrogenation is practically given

by k(r) of the rate-determining step itself, according

to 9.2.2 and 12.5.1, and that the rates of k(s) are given by eq (12.9) in the form of k{s ) o exp (— A t H(s)l

RT), where k(s) 0 and A*H{s) are constants appropriate to step s which are independent of temperature at constant partial pressures of reactants; the

former was already statistical mechanically evaluated, the latter alone remaining to be determined.

The rates A(s)’s are thus estimated in what follows.

13.1 Estimates of fc(I a )

It is inferred, as shown below, that A(Ia ) is practically infinite or inestimably higher than Vs, so that

y(C2 H4 ) is practically unity according to eq (12.19),

i.e.,

y(C2 H4)= 1. (13.1)

13.1.1. Table 17 shows that at 110 °C deuterium

atoms in ethylenes-d„ are in perfectly random

distribution. Those in hydrogens-c?„ are also in

random distribution, although not as precisely as in the case of ethylene, possibly just because of less

accuracy in the measurements (cf. 5.2.5 and 9.2.3).

Step I a and its reverse must be rapid enough to keep

the deuterium in ethylene in gas and in the adsorbed

state in random distribution throughout, as mentioned in 12.6.5, so that A: E = Jc E( a), since, otherwise,

the distribution of deuterium atoms should deviate

from the random one, as mentioned in 9. 2. 2. 5. The

atom fraction xH must also be near xH( a). Identifying

xE with *E( a) and xH with xH(a)> one finds the coefficient of f-(I a) in eq (12.33.c) to be zero, while that of

y_(II) in the same equation is finite, as derived from

table 17. The rate u + (I a) is thus practically infinite as compared with f_(II).

Step III is rate-determining in the experiment in

question, according to 9.2.3. The rate A(III) should,

in consequence, be lower than A(II) according to 12.5.1 (iii). We have, on the other hand, from eqs

(12.16)

f-(II) _ A(II)

f+(III) ~ y(H)A(III)

which shows that d_(II) is greater than t>+(III) ac- cording to 12.5.1 (i). Since f+(III) is practically equal

to the steady rate of hydrogenation, y+(Ia ) ^ K or by eq (12.16.Ia) A(Ia ) Vs

. 13.1.2. It is read from the results of Turkevich

et al. [1 17], as reviewed in 5.2.2, that

48
VS :VEl :VEn>i —1:2.33:0 (13. 2. E)

and

VAo :VKi :VA2 :VAn>i = 1:0.69: 0.154:0

(13. 2. A)

at the very beginning of the catalyzed deuteration

of light ethylene over nickel wire at 90 °C. Equation (13. 2. E) states that Ei is the only deuteroethyl- ene evolved at the very beginning, which shows that

the reverse of step I a

is rapid enough to carry away

Ei(a) once formed by step II and its reverse before

Ei(a) enters step II again to acquire another deuterium atom. Equation (13. 2. A) states, on the

other hand, that the only deuteroethanes evolved

are Ai and A2 . It follows, since ethane is formed

by two consecutive additions of H(a)’s to C2 H4 (a) according to scheme (9.5), that practically only

light C2 H4 (a) are subject to two consecutive additions, endorsing the statement of eq (13. 2. E) and,

in conjunction with the latter, confirming the conclusion of 13.1.1.

13.2 Estimate of k(I b )

It has been concluded in 9.2.3. that the rate- determining step below the optimum is I b

. The

quantity A*//(Ib ) is thus determinable from observations of Vs below the optimum identifying Vs with A(Ib ) of eq (12.9.Ib); the value

A*//(Ib ) = 4.7 kcal/mole (13.3)

is adopted; this is the mean of the two observations,

A*//(Ib) = 4.60 kcal/mole [64] and A*//(Ib ) = 4.80

kcal/mole [26].

13.3. Estimate

There are three methods of determining A:(III) through A* //(III). One is quite similar to that of

determining A*//(Ib ) in 13.2 on the basis of the conclusion in 9.2.3; this method has not, however, been

adopted, since the appropriate observations above

the optimum are not sufficiently reliable.

The second method consists in comparing a theoretical relation between Tx and PE with the observed relation (4.3); its result, described in 13.3.2,

is used for checking that of the third method adopted

here, which determines A(II) and /r(III) coherently

from the experimental results of eq (13.2), as described in 13.3.1.

13.3.1. The experimental results of eq (13.2) are stated in conjunction with the appropriate condition as

xE = 0, *Eo(a)=l, *„=1. (13.4.E), (13.4.E(a)), (13.4.H)

from which AAo( a ) and AAl ( a ) are deduced according to eq

(12.24.A) as

^Ao(a) 1 ^H(a)* ^Ai(a) ^H(a) and ^An>i (b

ignoring (1 — xH( a )AEi(a)> inasmuch as must be quite small according to eq (13.4.E(a)). We have, from the above equations

and eq (12. 31. A)

Tao = ( 1 - *H(a>) V(III), vA, — 2xH(a) ( 1 ~ *H(a) ) V+(III), U =4<a)"+(III) (13. 5. a)

and

Un>2 = 0, (13. 5. b)

from which the most probable value of *H(a) is determined by

eq (13. 2. A) as

*H(a>= 0.264. (13.6)

of fc(II) and /c(III)

4 The fraction %E(a) = ^7 rcAEn ( a)/4 may be ignored as compared

n= 1 with the above value of xH( a ), since the fractions A)E;i>0( a) are ex- tremely small according to eq (13.4.E(a)). We have thus from

eqs (12.23. a) and (13.4. H)

Mil) = 3

1 ~*H<a)

i; +(I b ), (13. 7. a) *H(a)

hence by eq (13.6)

v_(II) = 8.36 MU (13. 7. b) We have, on the other hand, from eq (12.21.E) for n = 1

2 ~As.(a)Mla) + ^

*H(a)MlI) = 0; (13.8)

the first term of eq (12.21.E) vanishes because of eq (13.4.E), since

4 xE = ^ nXEJ4; eq (13.8) is arrived at by ignoring all terms conn= 1 taining the factors AEl< a) and AE2( a), which are small according to eqs (13.4.E(a)) and (12.21.jc), except for the term — AMa^-dab on

account of the practically infinite magnitude of ii_(I a), as con- cluded in 13.1. VE , is given by eqs (13.8) and (12.31.E) as EEi = (2/3)x:H( a

)i>-(II), hence by eqs (13. 2. E) and (13.6) K= 3 x 2 33 *H(a>MII) = 0.0755 Mil) (13.9)

or, substituting Mil) from eq (13. 7. b) into eq (13.9), Vs = 0.632 MU

Noting that MIb) equals &(I b) by eq (12.16.Ib), we have from the

first and third members of eq (12.19) and the above equation

y(H) = 0.607. (13.10.H)

49
Writing eq (12.18) with special reference to step II as Fs =(i;+ (II)/ il(II) — 1 )n_(II) or, according to eq (12.16.11), as Fs =(y(C2H3y(H)/

ylC-iHs) — 1 )n_(II), we evaluate y(C2H5 ) using eqs (13.9), (13.10.H)

and (13.1) as

y(C2H5) = 0.564. (13. 10. A)

Equations (13.1) and (13.10) give, by eq (12.19), the ratio be- tween A(s)’s at 90 °C as

k{I„) : AUI) : A(III) = (1 — y(H)2

) -1

: (y(H) — y(C2 H3))_1

: (y(H)y(C 2 H5 ))" 1 = 1:14.7:1.84. (13.11) The quantities A //(II) and A

T //(III) are now determined according to eqs (13.3), (12.5), (12.9) and

(13.11), noting that /

3E =10 mm Hg and PH = 20

mm Hg in the experiment [117] in question, as

A*//(II) = — 12.6 kcal/mole, (13.12.11)

A

t //(III) = — 18.3 kcal/mole. (13.12.III)

13.3.2. The rate-determining step is switched over from step I b to III, when the temperature rises past

the optimum, according to 9.2.3. An equation for

the optimum temperature, Tx , is thus obtained by

equating k( I b) to A(III) at T = Tx in accordance with

eqs (12.9) as

A*//(Ib ) — A*//(III) = 2.3 RTX \og10QE ,olPE, which gives, on comparison with the observation

of eq (4.3),

A^//(Ib) — A

+ //(III) =24.2 kcal/mole (13.13.H)

and

logio@E ,o= 14.5. (13.13. Q)

We have, from eqs (13.3) and (13.13.H),

A+Z/(III) = — 19.5 kcal/mole,

which agrees tolerably well with the value of

(13. 12. Ill), confirming it thus, while the value of

eq (13.13.Q) is in excellent agreement with the

theoretical value log10 QE ,o= 14.596 of eq (12. 5. E).

13.4. Rates Based on the Estimated /e(s)’s

We have from eqs (12.9.Ib ), (12. 5. H) and (13.3)

Ogio b)- og10 P L057 x 1Q10 y~

(13.14.Ib) and similarly from eqs (12.9), (12.5) and (13.12)

for steps II and III

logio A;(II)

and

= logio p

pH \

1/2 PE 2751

1.057 X 1010/ 3.939 x 1014 T

(13.14.11)

1 WTTTX i ph Pe , 4008

Og!0 k(lll) logio Pj 057x 1Q10

* 3 939 x 10,4+ T

(13.14.III)

The rates k(s) determine Vs , y(H) and y(C2 H5) by eq (12.19) with reference to the values of y(C2 H6 ) given in 12.5 and y(C2 H4 ) of eq (13.1). These values

of A(s)’s and of y(C2 H4 ), y(H), y(C2H5) and y(C2 H6 ) determine z;+(s)’s and p_(s)’s by eqs (12.16) as shown in figure 27.

The rates Vs , Vex>E , Fex>H , Vp and Vq are hence

developed in terms of v+isj’s and v-(s)’s by eqs

(12.18), (12.26), (12.27), and (12.30); xH( a ), as required

for the calculation of VQI for *E = 0, ^r H =1/2 and

u — 0, is determined by an equation

xH(a) xEv-(U) + 3xHv+(Ib ) v-(II) + 3v+(Ib) (13.15)

obtained from eq (12.24.H) for infinite v+(I a) = A(I a). The' results are shown in figure 28, side by side

with k(s).

We see from figure 27 that v+(II) = f-(II) throughout, i.e., step II is practically in equilibrium. The

rates f+(Ib ) and t» + (III) coincide at lower temperatures but diverge above the optimum which is lo- cated around the intersection of Ac(I b) and Ar(III) in figure 28; n+(Ib) coincides above the optimum

with f-(I b) indicating an equilibrium of I b , while

p+(III) gives practically the steady rate of hydrogenation governed by step III in accordance with

12.5.1 (iii) and figure 28, f_(III) being vanishingly

small as seen in figure 27.

The following is inferred from the above numerical results.

13.4.1. Figure 27 shows that at or below 200 °C,

n-(III) is smaller than n+(III) by a factor of at least

106. Such a small rate, p_(III) is hardly traceable,

insofar as methods reviewed here are concerned.

This accounts for the results obtained by Matsuzaki and Nakajima [120] in 5.2.7 that ethane was

not perciptibly involved in the catalyzed hydrogenation.

13.4.2. Figure 27 shows that step III is far from

being in equilibrium over the temperature range

where I b determined the rate, according to 9.2.3.

50
Figure 27. Rates of steps s, v+(s), and of their reverses , v_(s), at the steady state of hydrogenation

over nickel

s = I b , II, III.

^

) e = /

) h = /,a= 10 mm Hg. p = kT^NJh.

It is inferred below that Ib actually satisfies the

conditions, advanced in 9.2.2, for a step determining the rate, notwithstanding a departure of some

other constituent step from equilibrium.

Comparison is made in this regard between the

magnitude of y_(Ib) in the steady state and that in

perfect equilibria of all steps other than I b

. The

rate y~(Ib ) in the respective case is given according

to eq (12.16.I b) as i>_(I b ) = y(H)iA'(Ib ) or t;_(I b)eq = y(H)|q

A-(I b), where suffixes s and eq signify the

particular values in the steady state and in the state of perfect equilibria of all steps but I b , respectively.

51
I0 3/T°K

Figure 28. Steady rates, Vs etc., of hydrogenation of ethylene over nickel defined by functions k(s): s = I„, II, III. Vs

: for hydrogenation. Vex , E . Vex , H : for exchange of ethylene and hydrogen, respectively. Vp

: for parahydrogen conversion. VQ: for equilibrium, xE = 0, equimolar 'H 2 —

D

2 mixture.

The coefficient y(H)s is determined by eqs (12.19)

and (13.14), referring to eq (13.1), whereas y(H)fq = y(C2 H6), as follows readily from eqs (12.16) by

equating v+(s) with v-(s) for all steps but I b

. We have thus, e.g., at T= 250 °K and PE = PH = 10

mm Hg, where I b governs the rate according to

12.5. l(iii), y(H)^=10-8 and y(H)fq = 10-18

, so that

y-(Ib)s is greater than v_(I b) eq by a factor of ca. 10 10

. This makes, however, practically no difference in the net rate, Vs — A(Ib)( 1 — y(H)2

), as given by eq

(12.19), illustrating the argument in 9. 2. 2.1.

52
14. Application of the Theory of the Associative Mechanism

Various phenomena concerned with the cata- associative mechanism developed in the foregoing

lyzed hydrogenation of ethylene will be accounted sections,

for systematically on the basis of the theory of the

14.1. Switchover in the Rate-Determining Step

At the switchover temperature, Tx , of the rate- determining step from I b to III, we have A-(I b )=A(III), as mentioned in 13.3.2, and hence from eqs (12.14)

A*G(Ib) = A*G(III),

i.e.. A* //(I b ) — A* //(III) = rx ( A* S(I b) — A* S(III))

and

At S(I b) — A*S(III) = Si(in)r — S]( Ib ) r = SE ,

hence from eq ( 12 . 7. E)

A*S(I b ) A*S(III) = /? In (Qe, ol

e)i

which amounts to 62.2 e.u. according to eq ( 12 . 5. E)

for PE =10 mm Hg. This difference of activation

entropy originates from the ethylene molecule

that I(s)r of step III possesses in excess over that of

l b , and compensates for the difference in activation

heats which amounts to 24 kcal, leveling A:(I b ) and

A;(III) at Tx . We see that, while k(si) and k{s2 ) for steps and 52 of different activation entropies equal each other at a certain temperature Tx, one of them is higher than

the other below Tx but lower than the other above

Tx. No such switchover in the relative magnitudes

of A

(

5 )

5 s can take place without a difference in

activation entropies. This difference arises now

only through difference in the systems I(s) r of the

steps, insofar as the present approximation goes,

as seen from eq (12.14.A*S). Steps 3 and 7 in scheme

(9.7) have the same I(5)r , i.e., C2 H4 + H2 , hence a switchover in the relative magnitudes of their rates with temperature can hardly occur, as mentioned

in 9.3.2.

It is nothing to be wondered at that the activation

entropy provides inertia of the reaction intrinsically on equal terms with the activation heats, that the

activation entropy must be algebraically smaller in case of an heterogeneous step which amounts to a

restriction of a system initially in a three dimensional phase to a surface phase such as to reduce

its phase volume by a factor of ca. 108 and that

heterogeneous steps, which are thus destined to have algebraically smaller activation entropies,

have smaller activation heats, or even negative

ones, in accordance with the so-called compensation effect, in as far as rates accessible to our measurements are limited to a narrow compass of

magnitude.

14.2. Activation Heat of Hydrogen Exchange

The activation heat of exchange of hydrogen has

been observed definitely to be greater than that of

hydrogenation, which disposed a number of authors

[2, 13, 68 , 116] to attribute to the exchange of

hydrogen some different sequence of steps from

that of hydrogenation, as reviewed in section 9. Figure 28 shows that the one and the same sequence

of steps of the associative mechanism leads necessarily to an excess of the activation heat of ex- change, RT2 d In EeXj H/dT, over that of hydrogenation; the excess amounts to 23 kcal below Tx = 373

°K and 5.7 kcal at 200 °C, qualitatively in accord- ance with the experimental results of Twigg and

Rideal [68]. The necessity of having this excess is qualitatively demonstrated on the basis of the associative

mechanism as follows. The exchange rate, Eex> H , is given in general by substitution of xH(a) from eq

(13.15) into eq (12.26.H) as Vex , H = 2v-(II)i;-(Ib)/(MlI) + 3f+(Ib )), (14.1)

which will be discussed now for the respective cases below and above the optimum.

The rate-determining step being either I b or III in accordance with 9.2.3, we have partial equilibrium of step II throughout, as verified by figure 27,

hence according to eqs (12.16.11) and (13.1)

y(H) = y(C2 H5 ). (14.2)

Equations (12.22.H) and (12.22. A) yield, on the other

hand, t>+(I b ) = v-ih) + f-(III) or, substituting f+(Ib) etc. from eq (12.16) and referring to eq (14.2), A:(I b) — y(H)2 (A(I b ) + A(III)).

In the temperature range below the optimum we

have ignoring A:(I b) as compared with A;(III),

y(H)2 = A;(I b

)/A:(III). (14.3)

Figure 27 shows, on the other hand, that y+ (II)=y-(II)

is far greater than i>+(I b ) while y+(Ib) equals f+(III),

i.e..

53
v+(III) = A(III) (14. 6. c)

f+(II) = v-(H) > y+(Ib ) - y+(IH). (14.4)

Ignoring thus i;+(Ib ) in comparison with f-(II), we

can reduce eq (14.1) to the form

Kx. h = 2u_(Ib ) (14.5.a)

or, according to eqs (12.16.Ib ) and (14.3),

Fex ,H = 2MIbm(III). (14.5. b)

Equation (14. 5. b) is interpreted as follows. Equation (14.4) shows that an H(a) formed by the forward

act of I b passes rapidly between the initial and final states of step II until it finally enters step III to finish the hydrogenation or the reverse of I b to revert to H2 in gas. Eex , H counts those H(a) (cf. eq (14.5 a)) which get back into hydrogen molecules

in gas per unit time, i.e., the rate of overall supply

of H(a), 2i>+(I b), multiplied by t>-(Ib)/(i>-(I b) + v+(III))

which is the fraction of them getting back into H2 , or by y_(Ib)/c+(III), according to eqs (12. 16. I b ), (14.4),

(14.3), which state that y_(Ib) = y(H)2

i> +(Ib) = f+(III)A:(I b )/A(III) y+(III). This fraction equals

A(Ib )/A(III) while v+(Ib ) is given by Ar(I b), hence

eq (14.5. b).

The activation heat of exchange of hydrogen,

RT2 d In VeXi u/dT, is hence necessarily greater than

that of hydrogenation, RT2 d In k(l b )/dT, by RT2 d In

k(lb)/dT — RT2 d In k(lll)ldT (below the optimum),

which is inevitably positive as shown in 14.1.

Above the optimum, where step III governs the

rate as concluded in 9.2.3, we have from eq (12.19),

according to inferences (i) and (ii) in 12.5.1 and to eq (13.1), that

y(H) = y(C2 H5 ) = 1, (14.6. a)

hence

v+(s)=v-(s)=k(s), s = Ia , Ib , II (14.6. b)

and

according to eqs (12.16), i.e., all steps but III are

in partial equilibrium. We observe the higher

extreme of temperature, where A(I b ) > A(II) as seen in figure 28. Equation (14.1) then assumes

the form,

Eex , H = (2/3)MID (14.7)

if we ignore u_(II) = A(II) as compared with 3u+(I b ) = 3A(I b ) and identify f_(I b ) with y + (I b ) = A(I b ). We have from eq (12.24.E), for the predominance

of u+(I a ) inferred in 13.1,

*E(a) = *E (14.8. E)

and from eq (13.15), for the predominance of

y+db) over y_(II),

*H(a) = *H- (14.8. H)

Equations (14.8) state that the “fall” of deuterium

content occurs across step II so that the rate of

exchange is proportional to y_(II) = v+(II) = A(II), as seen from eq (14.7); the proportionality factor

2/3 represents the number of hydrogen atoms

transferred from the state where they belong to C 2 H5 (a) back to that of H(a) for every reversal of

step II; this transfers either of the two hydrogen

atoms in the methyl radical originating from

C2 H4 (a) with the probability of 1/3; two out of three

times does the reversal bring hydrogen atoms from

C 2 H4 (a) to the state of H(a) as given by the proportionality factor.

The activation heat of exchange of hydrogen is thus RT2 d In A(II)/dr=At//(II) =-12.6 keal which

is algebraically greater than that of hydrogenation. — 18.3 kcal, but by an excess appreciably smaller

than that below the optimum.

14.3. Retardation of Parahydrogen Conversion and 1 H2 -D2 Equilibration

by the Presence of Ethylene

It may be noted that eq (12.27) for the parahydrogen conversion and eq (12.30) for the equilibration

apply irrespective of the presence or absence of

ethylene, insofar as these associated reactions are caused by step I b and its reverse and the hydrogen

desorbed is in equilibrium with respect to parahydrogen conversion or to 1 H2-D2 equilibration.

The rate of parahydrogen conversion in the

presence or absence of ethylene is equal according

to eq (12.27), to t>-(I b ). This assumes, in the absence

of ethylene, its particular value, A(I b ), in equilibrium

of I b according to eq (12.16.I b ). It follows that the

ratio of the rates of parahydrogen conversion in the

presence of ethylene, Fp(P), and in its absence.

VP(A), equals v~(I b )/k(l b ) or, according to eq

(12. 16.1 b ), Vp(P)/EP(A) = y(H)-, (14.9)

where y(H) is the activity coefficient of hydrogen

adatom in the presence of ethylene.

In the temperature range where I b governs the

hydrogenation rate, y(H) 2 is, according to eq (14.3),

extremely small as compared with unity, hence the

retardation of parahydrogen conversion by ethylene

according to eq (14.9). Above the optimum y(H)-= 1, according to eq (14. 6. a), hence no retardation. These

54
conclusions account for the observation [2] re- ferred to in 5.1.1. The rate of 1 H2-D2 equilibration, Vq , is given,

under the special condition where n = 0 and xE = 0,

according to eq (12.30), as

ts -t-H(a)(l ^H(a)) n \ y<x - — i—Mib ).

The value of *H(a) in the absence of ethylene is nothing but xH . We have thus, denoting the rates

in the presence and absence of ethylene by suffixes

(P) and (A), respectively:

Fq(P)/Fq(A> ^

-* H(al( 1 *H<a>) ^

*h(1 — xh ) The value of xH( a ) for xE = 0 is given by eq (13.15) as

3f +(I b) *H(a) _

f-(II) + 3t>+(I b) *H ' (14J1)

Below the optimum, ^H(a) is extremely small as compared with unity according to equations (14.11)

and (14.4), hence retardation; above the optimum,

where A(I b ) predominates over Ar(II), *H(a) equals xH according to equations (14.11) and (14. 6. b), hence

no retardation. The former conclusions explain the

experimental result [68] reviewed in 5.1.2.

14.4. The Relation Between Equilibrium Fraction, u, and

Deuterium Atom Fraction, xH, of Hydrogen

The theory of the associative mechanism leads

to the expression for u in terms of *H and *H(a)

exp / f

1 dxH \ _ \ JxH xH(a)~-y H/ f

1 *H(a)(l ~ -*H(a)) ^h( 1 Xh) Jxh X H ^H(a)

• exp ( [ — ) dxH (14.12)

\ J xH *H — XH( a )/

as derived in the following.

On elimination of Vex , H and f — (It>) from eqs (12.25.H), (12.26.H)

and (12.30), one obtains, noting n H = 2/VH by definition.

Lim u = rH( a), Lima— 1. (14. 13. a), (14.13. b)

XH

* 1 XH * *H<u) Equation (14.13) applies in the case of deuteration

of ethylene with pure deuterium, as in the experiment of Twigg and Rideal [68] reviewed in 5.1.2; part

(a) shows that u starts from the initial value of xH( a ). while part (b) indicates the situation, which is finally

arrived at along with the progress of reaction.

It is now required to find xH < a ) as a function of xH in order to determine the relation between u and

xH by eq (14.12). Th£ relation is given for a equimolar mixture of reactants as

*H — *H( a ) = Pexp jj (W)(Mb)/2

du _ X H(a)(l *H(al)

f/* H (^H(a) — *h)*h(1 — *h)

(-!— \ ^Hfa) X H

1 1\

1 — xH rn / u.

which is solved as

' dxh exp

rH *H(a) x

X H (1-XH ) -1/( Jj- H

^H(a) 1 1 *H(a X H *H(a)

exp

f

1 dxH

J JH x» — ^H(a) dxh + C [:

the integration constant, C, is determined by substituting u from

eq (12.29) into the above equation thus

jV-HD _ ( [' W

2/VH ^ W.rH XH( a ) — XW 1 J J'h

1 ^H(a)(l *H(al) *H ^H(a)

exp

Jjt fh

dxH XH ^H(a) dxH + C

+ v_(I b ) d In Pj. (14.14.JC)

where

F = MII)(t;-(II) + Sy+a,,))- 1 (14.14.F)

and P and Po are the current and the initial partial

pressures of either reactant. The fraction *H is given as a function of P, as

1 -xH =

J^

(Fv-(I b )/Vs) exp |— (F/Vs )

•(v+(Ib)/2 + v-(l b ))d In p

jd In P. (14.15)

Equations (14.14) and (14.15) are derived as follows.

Equation (12.25.xE ) is written, replacing z;_(I a) with u+(Ia ) ac- cording to equations (12.16.I a ) and (13.1), as

Since /V, HD = 0 for xH = 1, we have C = 0, hence eq (14.12) above.

Equation (14.12) leads to the following limiting

values of u as xH tends to unity or to xH( a >- respectively:

'J E^E == 4(xE( a ) —

E )t>+(I a ).

Eliminating (jc e — jc E(a) )i> + (I a ) and (* E(a) — *H(a>)t>-<II) from the above equation, eq. (12. 23. a) and (12.23.c), we have

Nxe = 1/2 (x H -JfH(a))i, + <lh). (14.16)

55
where N= n E /4 = n H/2 is the number of molecules of either reactant. The fraction. x H(a)- is substituted from eq (13.15) into eq (14.16) with reference to eq (14.14.F) as NxE =l/2 • (xH — xE )Fv+(l b ). (14.17) We have, on the other hand, from equations (12.25.H) and

(12.26.H)

A^H = (*H(a>-*H)tMlb) (14.18)

or. substituting Jf H(a> from eq (13.15) with reference to eq (14.14. F). NiH = {x E -xH )Fv-(l b ). (14.19)

Equations (14.17) and (14.19) lead to the differential equation — (x E — x H )/(x E — *H ) = (F/N)(v + (l b )/2 + v_(I b )),

or by integration to the equation

xE —xH = C exp

j —

J

(F/N)(v+(I b )/2 + u-(I b ))rft|,

where C is the integration constant as determined for the initial conditions, i.e., x E = 0 and xH = 1 at t = 0, as

— 1 = C exp j— J

{F/N)(v+(l b )l2 + v-(l b ))dt^,

hence

xH — xE = exp j— J{F/N)(v+(l b )l2 + v-(l b ))dt^.

The value x H —

x

E thus obtained is substituted into eq (14.19) as

xh =—(F[N)v-(I b ) exp j— J

(F7A0(t>+(I b )/2 + Mlb))dtj.

On integration we have

1 —xH =

J

(F/N)v~(I b ) exp j— J

(F/N)(v+(I b )/2 + v-(I b ))dt

j dt,

determining the integration constant by the initial condition that xH = 1 at t = 0. The last two equations are written, changing the variable of

integration for an expedient calculation according to the identity,

dt _ d In P\dt dt_—d\nP d In P

N~d In Nldt — dN/dt ~ V^~

based on the proportionality between P and N and the relation,

Vs = — dN/dt, as

xH = — (F/N)v-( I b ) exp j— J

°(F/Fs)(t;+ (I b )/2 + u_(I b))rflnPj

and as eq (14.15) above respectively; eq (14.14.x) is obtained by

substituting xH from the above equation into eq (14.18).

Figure 29 shows the relation between 1 — u and

xH calculated by eqs (14.12), (14.14), and (14.15) for

Pe, o = ^h, o 4= 10 mm Hg, which roughly reproduces

the experimental results of Twigg and Rideal [68]

in figure 16 on the one hand and predicts [8, 9, 10,

137] the rapid run down of the curves at lower

temperatures, on the other hand, which has been

verified by Matsuzaki [115] as shown in figure 17.

FIGURE 29. Theoretical relation between 1 — u and x H in course ofdeuteration oflight ethylene over nickel. Pe, o = f* h.o = 10 mm Hg, 1 — u : nonequilibrium fraction, u = ['HDJ/f'HDJeq, xH : atom

fraction of deuterium in hydrogen gas. The curves at 0 °C and —25 °C almost coincide with the vertical through xtt =\. The starting points of curves are Lim (1 — u) = 1 — jr H(a) according to eq (14.3. a) in

-*H

* 1 the text, and are indicated with horizontal arrows where not clearly recognizable.

14.5. Changes in Fa„’s With Temperature and Partial Pressures of the

Reactants

We have from eq (13.5)

^A0

' V

A

x

' V

A

2

• VAn>2 = (1 ~ *H(a))

2

: 2xH(a)( 1 - *H(a)) : *H(a) : 0. (14.20)

which shows that the relative magnitudes of Van depend solely on *H(a)- The fraction xH( a ) is now

uniquely defined, according to eq (13. 7. a), by the

ratio u + (I b)/r_(II) = k as

*H(a) __ v + (Ib) _

3(1—

H(a>) y -(H)

(14.21. a)

while k is expressed by eqs (12.16) as

K = A(I b )/y(C2 H5 )A-(II). (14.21. b)

56
Table 28. Theoretical values of initial evolution rates, VE[1 and VAn, of ethylenes-d n = En and ethanes-dn = An in the deuteration

product of light ethylene over nickel a

Temp.

°C

Initial partial pressures mm Hg

. K xH(a) eEi yEn>1 ^A0 rAl Va2 ^*>2

^E, 0 P\\,0

90 10 20 0.121 0.264 69.9(76) 0 16.2(13) 11.7(9) 2.2(2) 0 90 10 100 0.287 0.463 63.8 0 10.4 18.0 7.8 0 90 10 600 0.819 0.711 56.0 0 4.2 20.0 25.0 0 120 10 20 0.486 0.593 86.1 0 2.3 6.7 4.9 0

150 10 20 2.13 0.865 93.5 0 0.1 1.5 4.9 0

a Parenthesized figures show experimental result of Turkevich et al. [117]

The function k is determined by the values of k{s ) for the specified conditions according to eqs (13.14)

and y(C2 H5 ) derived from k(s) by eq (12.19). The

relative rates of eq (14.20) are thus calculated for

different values of PE , PH and temperature as shown

in table 28. The values at PE = 10 mm Hg, PH = 20

mm Hg and 90 °C closely reproduce the observations, shown in parentheses, by Turkevich et al. [117], under the same conditions.

We see from table 28 that the maximum yield

of ethanes-^ is shifted from A0 through Ai to A2 by either increasing PH/PE or raising the temperature. These conclusions have been experimentally

verified semiquantitatively by Miyahara and

Narumi [114] as shown in tables 15 and 16. The dominating factor k is discussed in what

follows. In case where I b determines the rate, we

have y(C2 H5 ) = y(H) = VA(Ib )/A(III) from eq (14.2)

and (14.3), hence by eq (14.21. b)

k = \/ki I b) A:( III)/ Af II) (14.22. a)

or, according to eqs (12.9) and (14. 22. a),

k cc VPJPl. (14.22. b)

Equations (14. 21. a) and (14.22.b) indicate that xH( a ) increases to shift the maximum yield of ethanes-d,,

toward A2 by increasing PH/PE in accordance with

table 28.

When the rate is determined by step III, at higher temperatures, we have from eqs (14.21.b)

and (14.6. a) k = A(I b

)/A:(II). The factor k increases

with temperature, since A*//(I b ) > A*A/(II) as seen from eqs (13.3) and (13.12.11), so that at sufficiently

high a temperature *H(a) tends to unity and the

maximum yield shifts to A2 ; there must, however,

be a range of temperatures, as seen in figure 28,

where step III determines the rate but /c(I b ) A(II),

hence A0 predominate.

14.6. “Random Distribution” of Deuterium in Ethylene and Ethane in the

Deuteration of Light Ethylene

Kemball [76] has observed the initial evolution

rates of ethylenes-d„ and ethanes-d„ in deuteration

of light ethylene over evaporated nickel film as referred to in 5.2.3. It is shown next that his results

follow necessarily from the present theory for the

associative mechanism.

The values of logio(A(.s)/p) are calculated for the

specified experimental conditions, i.e., —100 °C,

Pe = 2.7 mm Hg and PH = 8.1 mm Hg by eqs (13.14)

as

logio(A-(I b )/p) = 16.9543, logio(A(II)/p) = 2.1552,

log10 (A(III)/p) = 1.8604

from which y(C2 H4 ), y(H) and ylC^Hs) are evaluated

by eq (12.19), ignoring y^He) 31 and referring to

31 7(C 2 H6 ) = 4.5 X 10-30 was obtained as described in footnote 25 to 12.5 under the

specified experimental conditions, equating the partial pressure PA of ethane with PE \ T(C2Hk) vanishes for PA =0 by definition.

eq (13.1), as

y(C2 H4 ) = 1 , y(H) = y(C2 H5 ) = 3.52 x 10~ 8

.

The forward and backward rates, v+(sYs and t'_(5)’s, of steps s are calculated from the above values of

A’(s)’s and y(H) etc. according to eqs (12.16) as

f+(II) = f-(II) = 5.038 X 10" H

p, f+(I b ) = y+(III) = 9.002 X 10- 16p, MIb )= 1-118 X 10- 29p,

as given in the order of their magnitudes. Step II as well as step I a , in accordance with 13.1, are thus

occuring in both directions with rates far exceeding

those of other steps, so that an isotopic exchange

equilibrium is brought about among C2 H4 , C2 H4 (a) and H(a) according to the associative mechanism;

the deuterium atoms in C2 H4 (a) and H(a) are in

57
consequence in random distribution, hence as well

those in C2 H6 , which is composed of C^H^a) and

H(a) according to the mechanism. It follows that

ethylenes-rf,, are evolved with the relative rates

given by eqs (12.31.E) and (12.32), and ethane-^

by eq (12.33.c).

The above conclusion is compared with the ex- perimental results of Kemball [76] in table 29 in

terms of the percentages of ethylenes-c/„, (100 — 36.7)

•(^H(a)(1 -^H(a))

4 - n /2

~ *H(a))

4 “ and

of ethanes-c?,i, 36.7^%”(a) (l —xH(a)) 6-

", among the

total ethanes, and excellent agreement is found; 36.7

in the above expressions is the percentage of ethane

in the entire hydrocarbons excluding light ethylene,

and (^Wa^-W)4 -"/ 2 Q*&a)(1_ *H<a))

4 - n

is the fraction of the amount of ethylene-of« in the

total amount of ethylene excluding light ethylene.

The value of xH( a > was taken to be 0.222.

Wagner et al. [126], conducted an experiment, as referred to in 7.1.3, on the catalyzed deuteration of

light ethylene in the presence of nickel on kieselguhr

and observed the distribution of ethanes-fl?„ in the

product of the catalyzed deuteration. They tried to account for the experimental results assuming a random distribution of deuterium in ethane, i.e., in

accordance with eq (12.33. c); the maximum yield

of ethanes-(fn was thus located at n — 2 for —50 °C

but at n = 3 for 50 °C, whereas the maximum was

observed at n — 2 in both cases [126]. Wagner et al., calculated xA to be 0.35 and 0.50 at —50 °C and

50 °C, respectively, as the fraction of the total

number of deuterium atoms lost from hydrogen

gas over the total number of hydrogen atoms in

ethane evolved. Since no deuterium entered ethylene, this process of calculation would be correct,

provided only that the supported catalyst did not

exchange deuterium with reactants. Without relying on the assumption xA is straightforwardly and nec6 essarily given as xA = 2 n^\ /6. The fraction. xA , n = 1 is thus calculated as 0.331 and 0.422, respectively,

at —50 and 50 °C. With these values, the observed

peaks at n — 2 are reproduced at both temperatures.

Table 29. Relative rates of evolution, VEn and VAn , of ethylenes-dn = En and ethanes- d n = An in the initial deuteration product of

light ethylene over evaporated nickel film PE , o = 2.7 mm Hg, PH . o = 8.1 mm Hg, — 100 °C

xH(a ) V“3E vEt vA o vA Va4 vA

Obs. [76]

a 46.7 13.2 2.7 0.7 7.8 12.5 9.5 4.0 2.0 0.8 0.2 Calc. b 0.222 41.8 17.9 3.4 0.3 8.1 13.9 9.9 3.7 0.8 0.1 0.0

a Reproduced from table 12.

b The percentages are calculated according to eqs (12.31.E), (12.32) and (12.33.c), and the experimental result that the total ethanes

amounts to 36.7 percent of the total hydrocarbons except E0 , as

^e „ = (100-36.7) ^ (^)^(a) d-^E(a,)

4 -

and VAn = 36.7 *»(1-*a)6 -". assuming xE(a ) = xA = xH( a) .

14.7. Isotopic Effect on Hydrogenation Rate

We have seen in section 6 that the hydrogenation

rate of light ethylene with light hydrogen exceeds

the deuteration rate of light ethylene under similar

conditions by a factor of 2 to 3 at temperatures below the optimum; the factor decreases down to unity around the optimum temperature but exhibits

a tendency to increase again at higher temperatures

as seen in figures 19, 22, and 23 or in table 20. The

experimental results are accounted for by the

present theory as follows.

We see from figure 28 that step I b governs the

rate below the optimum, hence the appropriate

isotopic difference in rate. Above the optimum,

the rate is governed by step III, hence an isotopic

difference in rate depending on *H(a), while the

fraction *E( a ) is kept equal to xE = 0 as inferred in

13.1. The fraction jt H(a) for jce = 0 is now given

according to eq (14.11), which is written for temperatures above the optimum according to eq (14. 6. b) as xH( a )= {‘3k(l b)/{k(ll) + 3k{lb))} xH . There are two

phases, one at lower and one at higher temperatures

in the region of rate-determining step III, where

A:(I b ) < Mil) and A(I b) > MU), respectively, as seen from figure 28. The above equation states that at the lower temperatures in this region, xH( a ) is small even in the case of deuteration, and affects little the rate-determining step III isotopically, whereas

at higher temperatures *H(a) approaches xH = 1 and

hence makes an isotopic difference through the

rate-determining step III in accordance with ex- perimental results.

58
15. Application of the Theory of Absolute Rates

Laidler [138] applied the theory of absolute rates

to the rate-determining step III of the associative

mechanism and to a step

2C2 H5 (a) C2 H4 (a) + C2 H6 , (15.1)

concluding that a tolerable agreement with experimental results is obtained in both cases. His procedure and conclusion are commented upon on the

basis of the present theory.

15.1. Laidler expressed the concentration CS2 of dual sites, i.e., the number of pairs of adjacent

bare sites per unit area of catalyst as

CS2 = sCs2I2L,

where Cs is the concentration of bare single sites,

5 the number of sites adjacent to a single site and

L the concentration of single sites when the surface

is completely bare. This equation is derived ex- pressing the probability that one of adjacent single

sites to a bare single site is also bare, by 1 — 6 , where 0 is given by 2Ca\L in terms of the concentration Ca of adsorbed ethylene. This procedure

would be exact, if C2 H4 (a) were dissociated into

adsorbed methylene radicals, CH2 (a), and distributed over single sites independent of each other.

Let 1 and 2 be the adjacent single sites, of which

the above probability is in question. The probability that site 2 is occupied under the premised

bareness of site 1 is 5- 1\

~) 6, since the premised

bareness of site 1 excludes one of s cases where

site 2 is occupied by an C2 H4(a) lying across sites

5—1

1 and 2. The probability in question is thus 1 6

5 rather than 1 — 6. The approximation associated

with the revised expression is that the probability

of the remaining s — 1 cases of site 2 being occupied

is assumed unchanged by premising the bareness

of site 1 thus excluding the one of s cases. This

correction changes, however, hardly the order of

magnitude of the numerical factor in question below.

We will remain, on that account, with Laidler’s

approximation in this regard.

15.2. A rather serious difficulty is associated with

this treatment in the temperature change of rate. Laidler arrives at rate equations of step III of the

associative mechanism and of step (15.1) respectively determining the rate, which contain numerical

factors, AB 2 and A 2B 2

, respectively, where

x = 2sKCg (15.4)

K = CalCgCS2 ; (15.5)

K is the equilibrium constant of adsorption and

Cg is the concentration of ethylene in gas here given

in terms of its partial pressure in mm Hg.

The procedure of Laidler to be questioned is this. He took arbitrarily the maxima of AB 2 and

A

2B 2 with respect to x for the calculation of reaction

rates. Since K varies with temperature, x will too, so that the numerical factors necessarily slip off

the maximum at a particular temperature, when

varying the temperature. The result is that the

temperature change of the numerical factor is superimposed upon that due to the Boltzmann

factor of a constant energy increment included in

the rate equation.

This superimposition is illustrated with the observation of Farkas, Farkas, and Rideal [2] at 120 °C

and PE = 12 mm Hg with which Laidler compares

his calculated rates. The last mentioned energy

increment is taken to be 4.7 kcal/mole by Laidler.

AB 2 and A 2B 2 have maximum values at around

x = 2 according to eqs (15.3). These maxima are taken to be numerical factors in calculating the

rates in the respective case. The K value for x — 2

and 5 = 4 is according to eq (15.4)

A= 1/(4 X 12) (mm Hg) ~

K can be written, on the other hand, in terms of

the heat of adsorption, e E , and of the partition function of ethylene, QE ,o, as done by Laidler with the

adsorption of hydrogen, as K= Qe, o exP UeAR^)- (15.6)

We have from the above equations and the numerical value of Qe, o of eq (12. 5. E)

eE = 23.2 kcal/mole. (15.7)

It follows from eqs (15.6) and (15.7) that K and in

consequence x decrease according to eq (15.4)

monotonously with increase of temperature.

It is readily deduced from eqs (15.3) that extreme

values of the numerical factors are

A =

1 + x — (1 + 2*) 1 / 2 2x

B _ (\ + 2x)^2 -l

AB2 = x~\A 2B 2 =(2x)-' for x > 1 (15.8.a)

and

(15.3.A), (15.3.B) AB2 = xl4, A 2B 2 = x

2 /16 lorx<l. (15.8.b)

59
We have from eqs (15.4), (15.6), (15.7), and (15.8)

that

RT2 d In ( AB2 )/dT=RT2 d\n ( A

2B 2 )/dT = 23.2 kcal/mole

in the extreme of low temperature and

RT2 d In {AB 2

) /dT=— 23.2 kcal/mole,

RT2 d In (A 2 B 2

) ldT= — 46.4 kcal/mole

in the extreme of high temperature. These amazing

values are inevitably superimposed upon the constant energy increment mentioned above. The

activation heat thus decreases from the low ex- treme of temperature to the high extreme by 46.4

kcal/mole in case of the rate determined by step

III and by 69.6 kcal/mole in case of the rate determined by step (15.1).

Such a superimposition occurs, however, over

not very wide a range of temperature; we have for

example

RT2 d In (AB 2

) /dT= 16.5 kcal/mole,

RT2 d In (A 2B 2

) /dT— 13.1 kcal/mole

at 90 °C and

RT2 d In (AB 2

) ldT=— 14.9 kcal/mole,

RT2 d In (A 2 B

2 )/dT=- 33.9 kcal/mole

at 150 °C as calculated by eqs (15.3), (15.4), (15.6),

and (15.7) assuming x — 2 at 120 °C. This amounts

to saying that nearly 70 percent of the overall

decreases of activation heat mentioned above are

got through within the temperature range of

±30 °C, which is far from being true.

15.3. One might try to elude the extravagant

superimposition inherent to the Laidler’ s procedure

by localizing the phase of the numerical factor

either to that of (15. 8. a) or (15. 8. b). In the former

case we have according to eqs (15.4) and (15.6)

AB2

~2scl exp

A 2B2 =j^irexp (—eEIRT). 4sG g

Incorporating the exponential factor in the above

equation in that of the activation heat as did by

Laidler with the adsorption heat of hydrogen, the

numerical factor is now (l/2s)(QE< olCg) or (l/4s)

((?e,o/Cj,), which amounts to 4.1 X 10 12 or 21 X 10 12 respectively for s = 4 and Pe~ 12 mm Hg. In the

latter case of eq (15. 8. b), the numerical factor is

AB2 = -^—= 6.1 X10-14 (15.9.a),

^VE. 0

or A

2B2 =(itbh3JX 10-27 (15Ab)

respectively for step III or (15.1) determining the

rate in place of the maximum value, 0.074 or 0.0156

used by Laidler. The agreement with experimental

results is thus quite out of question.

One might see that the numerical factors are secured in the order of magnitude of unity by confining them to the intermediate phase, say to their

maxima, where we encounter the difficulty described in 15.3.

15.4. The rate equation in case of step III determining the rate for x < 1 is given 32 according to eq (15. 9. a) as

v = ( kT/h)Nt (Cg/QEt 0) (Cg'IQn.o)

•exp(-A*H(r)/RT), (15.10)

where Nt represents (s/2)L i.e., the concentration

of dual sites in case of a practically bare surface,

Qe,o or <2h,o the partition function of ethylene or hydrogen and A*//(r) the activation heat. The

difficulty, in particular, with eq (15.10) is that v is smaller than that observed by a factor ca. 10 13 provided that Ax H(r) is fixed at 4.7 kcal/mole as assigned by Laidler. This difficulty is got over by

excluding ethylene from I(r)r of eq (12.13), which

reduces the rate remarkably by decreasing At S(r)

as seen from eqs (12.14) and (12.15). We are thus

just in fine with the association mechanism, in

which the rate is determined by the dissociative

adsorption of hydrogen molecules, i.e., by step I b , under the activation heat of the above magnitude.

The A*.S(III) is lower than A* S(Ib) on account of an ethylene molecule comprised in I(III)r in excess

over I(I b) r . Since /c(III) must, however, be greater

than A:(I b ) in the temperature range, where I b governs

the rate according to 12.5.1.(iii), step III should

have an activation heat sufficiently lower than step

I b in accordance with eq (12.14). Along with rise of

temperature, however, the effect of the lower

activation heat is reduced and sooner or later A(III)

becomes lower than A:(I b) so that III governs the

rate in place of I b at higher temperature according

to 12.5. l.(iii), hence the switchover in the rate- determining step described in 14.1.

J! We have an extra factor s

2 by a direct substitution of AB- from eq (15.9. a) into eq (91) of the article of Laidler (138]. He identified the partition functions, /„•»* and f„a \

in the last-mentioned equation of him respectively with unity, which is not correct, since the appropriate states are respectively s-fold degenerated. Equation (15.10)

is obtained without the extra factor by identifying partition functions /„» and /„„• respectively with s instead on this account. Detailed account will not be given on this point since the factor in question does not affect the conclusion.

60
16. Concluding Remark

As developed in the foregoing sections, the

present theory based on scheme (9.5) accounts

systematically for the experimental results on the

catalyzed hydrogenation of ethylene in the presence

of metallic catalysts especially nickel. But it may

be mentioned in concluding this review that the

present theory accounts for the experimental

results of other olefines as well, e.g., the optimum

temperatures observed in the catalyzed hydrogenation of propylene [139, 140] and butylene [141], the

distribution of deuterium in their deuteration

products [139], the migration of double bonds [141]

etc.

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